When do quasi-cyclic codes have $\\mathbb F_{q^l}$-linear image?

Authors : R NEKOOEI, Z POURSHAFIEY

Pages : 77-86

Doi:10.24330/ieja.1198011

View : 23 | Download : 10

Publication Date : 2023-01-09

Article Type : Research Paper

Abstract :A length $ml$, index $l$ quasi-cyclic code can be viewed as a cyclic code of length $m$ over the field $\\mathbb F_{q^l}$ via a basis of the extension $\\mathbb F_{q^l}/\\mathbb F_{q}$. This cyclic code is an additive cyclic code. In [C. Güneri, F. Özdemir, P. Solé, On the additive cyclic structure of quasi-cyclic codes, Discrete. Math., 341 insert ignore into journalissuearticles values(2018);, 2735-2741], authors characterize the $insert ignore into journalissuearticles values(l,m);$ values for one-generator quasi-cyclic codes for which it is impossible to have an $\\mathbb F_{q^l}$-linear image for any choice of the polynomial basis of $\\mathbb F_{q^l}/\\mathbb F_{q}$. But this characterization for some $insert ignore into journalissuearticles values(l,m);$ values is very intricate. In this paper, by the use of this characterization, we give a more simple characterization.
Keywords : Cyclic code, quasi cyclic code, additive cyclic code, linear code