How many weights can a linear code have ?
| Autor: | Shi, Minjia, Zhu, Hongwei, Solé, Patrick, Cohen, Gérard D. |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Designs, Codes and Cryptography, 2018 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10623-018-0488-z |
| Popis: | We study the combinatorial function $L(k,q),$ the maximum number of nonzero weights a linear code of dimension $k$ over $\F_q$ can have. We determine it completely for $q=2,$ and for $k=2,$ and provide upper and lower bounds in the general case when both $k$ and $q$ are $\ge 3.$ A refinement $L(n,k,q),$ as well as nonlinear analogues $N(M,q)$ and $N(n,M,q),$ are also introduced and studied. |
| Databáze: | arXiv |
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