A class of binary cyclic codes with optimal parameters

Autor: Kaiqiang Liu, Qi Wang, Haode Yan
Rok vydání: 2021
Předmět:
Zdroj: Cryptography and Communications. 14:663-675
ISSN: 1936-2455
1936-2447
DOI: 10.1007/s12095-021-00548-1
Popis: For positive integers k ≥ 2 and t, let m = 2kt and α be a primitive element of the finite field $\mathbb {F}_{2^{m}}$ . In this paper, we study the parameters of a class of cyclic codes $\mathcal {C}_{(1,v)}$ which has two zeros α and αv with $v=\frac {2^{m}-1}{2^{t}+1}$ . It is shown that $\mathcal {C}_{(1,v)}$ is optimal or almost optimal with respect to the sphere packing bound. Based on some results of Kloosterman sums and Gaussian periods, the weight distribution of the dual code of $\mathcal {C}_{(1,v)}$ is completely determined when t = 5.
Databáze: OpenAIRE
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