How many weights can a linear code have ?

February 01, 2018 · Declared Dead · 🏛 Designs, Codes and Cryptography

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Authors Minjia Shi, Hongwei Zhu, Patrick Solé, Gérard D. Cohen arXiv ID 1802.00148 Category cs.IT: Information Theory Citations 27 Venue Designs, Codes and Cryptography Last Checked 3 months ago
Abstract
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.
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