Name
Title | ||
|---|---|---|
Encoding Via Grobner Bases And Discrete Fourier Transforms For Several Types Of Algebraic Codes |
Abstract | ||
|---|---|---|
We propose a novel encoding scheme for algebraic codes such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed-Solomon codes and present numerical examples. We employ the recurrence from the Grobner basis of the locator ideal for a set of rational points and the two-dimensional inverse discrete Fourier transform. We generalize the functioning of the generator polynomial for Reed-Solomon codes and develop systematic encoding for various algebraic codes. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1109/ISIT.2007.4557619 | 2007 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-7 |
Keywords | Field | DocType |
feedback,inverse problems,encoding,linear code,polynomials,decoding,generators,information science,multidimensional systems,algebraic curves,finite element methods | Discrete mathematics,Combinatorics,Dimension of an algebraic variety,Polynomial,Algebra,Computer science,Algebraic curve,Block code,Reed–Solomon error correction,Linear code,Gröbner basis,Discrete Fourier transform | Journal |
Volume | Citations | PageRank |
abs/cs/070 | 2 | 0.40 |
References | Authors | |
5 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hajime Matsui | 1 | 18 | 8.14 |
| Seiichi Mita | 2 | 316 | 38.88 |