Fast decoding of codes from algebraic curves
The author shows how the fast decoding algorithm of Justesen et al. (1989), for codes from algebraic plane curves, can be extended such that codes from curves in an r-dimensional space can be decoded. He shows how Sakata's (1990) Berlekamp-Massey (1969) extension can be used to find an error lo...
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| Vydáno v: | IEEE transactions on information theory Ročník 40; číslo 1; s. 223 - 229 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York, NY
IEEE
01.01.1994
Institute of Electrical and Electronics Engineers |
| Témata: | |
| ISSN: | 0018-9448 |
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| Abstract | The author shows how the fast decoding algorithm of Justesen et al. (1989), for codes from algebraic plane curves, can be extended such that codes from curves in an r-dimensional space can be decoded. He shows how Sakata's (1990) Berlekamp-Massey (1969) extension can be used to find an error locator polynomial, and also shows that the cost of doing this increases with the dimension of the space. Unfortunately, the error-correcting capability gets worse for codes from curves in higher dimensional spaces. For a specific curve, he determines the error values faster than by solving linear equations. The method is an extension of the transformation method known from cyclic codes.< > |
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| AbstractList | The author shows how the fast decoding algorithm of Justesen et al. (1989), for codes from algebraic plane curves, can be extended such that codes from curves in an r-dimensional space can be decoded. He shows how Sakata's (1990) Berlekamp-Massey (1969) extension can be used to find an error locator polynomial, and also shows that the cost of doing this increases with the dimension of the space. Unfortunately, the error-correcting capability gets worse for codes from curves in higher dimensional spaces. For a specific curve, he determines the error values faster than by solving linear equations. The method is an extension of the transformation method known from cyclic codes The author shows how the fast decoding algorithm of Justesen et al. (1989), for codes from algebraic plane curves, can be extended such that codes from curves in an r-dimensional space can be decoded. He shows how Sakata's (1990) Berlekamp-Massey (1969) extension can be used to find an error locator polynomial, and also shows that the cost of doing this increases with the dimension of the space. Unfortunately, the error-correcting capability gets worse for codes from curves in higher dimensional spaces. For a specific curve, he determines the error values faster than by solving linear equations. The method is an extension of the transformation method known from cyclic codes.< > |
| Author | Dahl, C. |
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| Cites_doi | 10.1109/18.57204 10.1109/18.32157 10.1109/TIT.1969.1054260 10.1016/0890-5401(90)90039-K 10.1109/18.108255 10.1109/18.45279 |
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| Keywords | Algebraic code BCH code Decoding Fast algorithm Coding |
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| Snippet | The author shows how the fast decoding algorithm of Justesen et al. (1989), for codes from algebraic plane curves, can be extended such that codes from curves... |
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| SubjectTerms | Applied sciences Coding, codes Costs Decoding Equations Error correction Exact sciences and technology Geometry Information, signal and communications theory Polynomials Signal and communications theory Telecommunications and information theory |
| Title | Fast decoding of codes from algebraic curves |
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