On self-dual affine-invariant codes
| Autor: | Françoise Levy-Dit-Vehel, Pascale Charpin |
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| Rok vydání: | 1994 |
| Předmět: |
Discrete mathematics
Code (set theory) Polynomial code Binary number 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology 01 natural sciences Linear code Theoretical Computer Science Set (abstract data type) Computational Theory and Mathematics 010201 computation theory & mathematics Cyclic code 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Binary code Hamming code Mathematics |
| Zdroj: | Journal of Combinatorial Theory, Series A. 67:223-244 |
| ISSN: | 0097-3165 |
| Popis: | An extended cyclic code of length 2m over GF(2) cannot be self-dual for even m. For odd m, the Reed-Muller code [ 2 m , 2 m−1 , 2 (m+1) 2 ] is affine-invariant and self-dual, and it is the only such code for m = 3 or 5. We describe the set of binary self-dual affine-invariant codes of length 2m for m = 7 and m = 9. For each odd m, m ⩾ 9, we exhibit a self-dual affine-invariant code of length 2m over GF(2) which is not the self-dual Reed-Muller code. In the first part of the paper, we present the class of self-dual affine-invariant codes of length 2m over GF(2r), and the tools we apply later to the binary codes. |
| Databáze: | OpenAIRE |
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