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Designs, Codes and Cryptography

Erschienen in:

05.05.2018

How many weights can a linear code have?

verfasst von: Minjia Shi, Hongwei Zhu, Patrick Solé, Gérard D. Cohen

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1/2019

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Abstract

We study the combinatorial function L(k, q), the maximum number of nonzero weights a linear code of dimension k over \({\mathbb {F}}_q\) 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.

Vorheriger Artikel Polynomial interpolation of the generalized Diffie–Hellman and Naor–Reingold functions

Nächster Artikel Improved bounds on 2-frameproof codes with length 4

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Titel: How many weights can a linear code have?
verfasst von: Minjia Shi
Hongwei Zhu
Patrick Solé
Gérard D. Cohen
Publikationsdatum: 05.05.2018
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-018-0488-z

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