1. A method of encoding a data segment with a transform matrix for storage to a memory, the method comprising:
inputting a data segment into a non-systematic error correction code (ECC) transform matrix to output a non-systematic ECC encoded data segment, wherein the transform matrix distributes the ECC encoding across the non-systematic ECC encoded data segment; and
storing the non-systematic ECC encoded data segment to the memory.
2. The method of claim 1, wherein inputting a data segment into a non-systematic ECC transform matrix to output a non-systematic ECC encoded data segment further comprises inputting a data segment into a non-systematic ECC transform matrix to output a non-systematic ECC encoded data segment, where the transform matrix does not contain a unity core square matrix.
3. The method of claim 1, wherein inputting a data segment into a non-systematic ECC transform matrix to output a non-systematic ECC encoded data segment further comprises inputting a data segment into a non-systematic ECC transform matrix to output a non-systematic ECC encoded data segment, where the transform matrix localizes the ECC codes generated in the encoding in two or more areas in the non-systematic ECC encoded data segment.
4. The method of claim 1, wherein the non-systematic ECC code encoded with is one of a non-systematic Hamming code, a non-systematic Reed-Solomon (R-S) code, a non-systematic Bose-Chaudhuri-Hocquenghem (BCH) code, a non-systematic circular redundancy code (CRC-32), a non-systematic Golay code, a non-systematic Reed-Muller code, a non-systematic Goppa code, and a non-systematic Denniston code.
5. A memory system, comprising:
at least one memory device, wherein the at least one memory device contains a memory array with a plurality of memory cells arranged in one or more data segments;
a memory control circuit coupled to the at least one memory device, wherein the memory control circuit is configured to input a data segment into a non-systematic error correction code (ECC) transform matrix and to encode the data segment with the non-systematic ECC transform matrix to generate a non-systematic ECC encoded data segment, wherein the non-systematic ECC transform matrix distributes the ECC encoding across the non-systematic ECC encoded data segment, and to store the non-systematic ECC encoded data segment to a memory device of the at least one memory device.
6. The memory system of claim 5, wherein the memory control circuit is configured to encode the data segment by inputting the data segment into the non-systematic ECC transform matrix to output the non-systematic ECC encoded data segment.
7. The memory system of claim 6, wherein the non-systematic ECC transform matrix does not contain a unity core square matrix.
8. The memory system of claim 6, wherein the non-systematic ECC transform matrix localizes the ECC codes generated in the encoding in two or more areas in the non-systematic ECC encoded data segment.
9. The memory system of claim 5, wherein the memory control circuit is further configured to encode the data segment with one of a non-systematic Hamming code, a non-systematic Reed-Solomon (R-S) code, a non-systematic Bose-Chaudhuri-Hocquenghem (BCH) code, a non-systematic circular redundancy code (CRC-32), a non-systematic Golay code, a non-systematic Reed-Muller code, a non-systematic Goppa code, and a non-systematic Denniston code.
10. A memory device comprising:
a memory array containing a plurality of memory cells arranged into a plurality of segments;
a data buffer;
a host transfer circuit coupled to the data buffer; and
an error correction code (ECC) generatorchecker circuit, wherein the memory device is adapted to input a data segment into a non-systematic ECC transform matrix and to encode the data segment with the non-systematic ECC transform matrix and store the non-systematic ECC encoded data segment to the memory array, wherein the non-systematic ECC transform matrix distributes the ECC encoding across the non-systematic ECC encoded data segment, and wherein the ECC generatorchecker circuit is adapted to receive and decode the non-systematic ECC encoded data segment from the memory array and output to the data buffer.
11. The memory device of claim 10, wherein the memory device is configured to encode the data segment by inputting the data segment into the non-systematic ECC transform matrix to output a non-systematic ECC encoded data segment.
12. The memory device of claim 11, wherein the non-systematic ECC transform matrix does not contain a unity core square matrix.
13. The memory device of claim 11, wherein the non-systematic ECC transform matrix localizes the ECC codes generated in the encoding in two or more areas in the non-systematic ECC encoded data segment.
14. The memory device of claim 10, wherein the memory device is further configured to encode the data segment with one of a non-systematic Hamming code, a non-systematic Reed-Solomon (R-S) code, a non-systematic Bose-Chaudhuri-Hocquenghem (BCH) code, a non-systematic circular redundancy code (CRC-32), a non-systematic Golay code, a non-systematic Reed-Muller code, a non-systematic Goppa code, and a non-systematic Denniston code.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
What is claimed is:
1. In an objective lens having aspheric surfaces at both surfaces, used in an optical system in which light having a first wavelength is converged to the data recording surface of a first optical disk and reflection light from the data recording surface of the first optical disk is received by a light receiving element in recording or reading the first optical disk, and light having a second wavelength which is different from the first wavelength is converged to the data recording surface of a second optical disk and reflection light from the data recording surface of the second optical disk is received by the light receiving element in recording or reading the second optical disk, the objective lens being characterized in that:
a phase shifter provided with annular step portions W having a center coincident with an optical axis of the lens is formed in a single or both surfaces of the objective lens, wherein the phase shifter has function to produce a phase difference for reducing the aberration resulted in recording or reading the first optical disk with respect to the light having the first wavelength, and has function to produce a phase difference for reducing the aberration resulted in recording or reading the second optical disk with respect to the light having the second wavelength.
2. The objective lens according to claim 1, wherein a step portion X having function to produce a phase difference with respect only to the light having the first wavelength is formed in a single or both surfaces of the objective lens, the step portion X being an annular step portion X having the center coincident with the optical axis.
3. The objective lens according to claim 1, wherein a step portion Y having function to produce a phase difference with respect only to the light having the second wavelength is formed in a single or both surfaces of the objective lens, the step portion Y being an annular step portion Y having the center coincident with the optical axis.
4. The objective lens according to claim 1, wherein convex portions or concave portions are formed in a single or both surfaces of the objective lens to constitute a part of or the whole of the step portions W.
5. The objective lens according to claim 1, wherein dimensions and a shape of the step portions W of the phase shifter are determined so that the phase difference caused by light having a first wavelength 1 is from (i0.1)2 to (i0.1)2 when the phase difference is converted into a distance, and the phase difference caused by light having a second wavelength 2 is from (j0.1)1 to (j0.1)1 when the phase difference is converted into a distance, where i represents a natural number and j represents a natural number.
6. The objective lens according to claim 1, wherein the relation of 8NWNXNY13 is established among the number NWof annuli in the step portions W, the number NX of annuli in a step portion X and the number NY of annuli in a step portion Y, where NWrepresents a natural number, NX represents 0 (zero) or a natural number and NY represents 0 (zero) or a natural number.
7. The objective lens according to claim 1, wherein the objective lens is used in an optical system in which light having a first wavelength 1 and light having a second wavelength 2 are both converged to the data recording surface of an optical disk via an auxiliary lens and an objective lens, the objective lens being characterized in that:
a combination of the auxiliary lens, an aspheric surface in the surface including an apex in a surface of the objective lens and an aspheric surface in the surface including an apex in the other surface of the objective lens is determined so that the on-axial spherical aberration is from 0.08 1 to 0.25 1 in RMS value in a case that data in the data recording surface of the first optical disk are recorded in or read, and that the on-axial spherical aberration is from 0.08 2 to 0.25 2 in RMS value in a case that data in the data recording surface of the second optical disk are recorded in or read.
8. The objective lens according to claim 7, wherein the auxiliary lens is a collimeter lens.
9. The objective lens according to claim 1, wherein the objective lens is used in an optical system in which light having a first wavelength and light having a second wavelength are both converged to the data recording surface of an optical disk via an objective lens without being passed through an auxiliary lens, the objective lens being characterized in that:
a combination of an aspheric surface in the surface including an apex in a surface of the objective lens and an aspheric surface in the surface including an apex in the other surface of the objective lens is determined so that the on-axial spherical aberration is from 0.08 1 to 0.25 1 in RMS value in a case that data in the data recording surface of the first optical disk are recorded in or read, and that the on-axial spherical aberration is from 0.08 2 to 0.25 2 in RMS value in a case that data in the data recording surface of the second optical disk are recorded in or read.
10. In an optical device in which light having a first wavelength is converged to the data recording surface of a first optical disk via an objective lens and reflection light from the data recording surface of the first optical disk is received by a light receiving element in recording or reading the first optical disk, and light having a second wavelength which is different from the first wavelength is converged to the data recording surface of a second optical disk via the objective lens and reflection light from the data recording surface of the second optical disk is received by the light receiving element in recording or reading the second optical disk, the optical device being characterized in that:
the objective lens is an objective lens described in claim 1.