On a family of linear MRD codes with parameters $$[8\times 8,16,7]_q$$

Autor:	Marco Timpanella, Giovanni Zini
Rok vydání:	2023
Předmět:	FOS: Computer and information sciences Algebraic varieties Information Theory (cs.IT) Linearized polynomials Computer Science - Information Theory Applied Mathematics FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) MRD codes Computer Science Applications
Zdroj:	Designs, Codes and Cryptography.
ISSN:	1573-7586 0925-1022
Popis:	In this paper we consider a family $\mathcal{F}$ of $16$-dimensional $\mathbb{F}_q$-linear rank metric codes in $\mathbb{F}_q^{8\times8}$, arising from the polynomial $x^{q^s}+\delta x^{q^{4+s}}\in\mathbb{F}_{q^8}[x]$. Examples of MRD codes in $\mathcal{F}$ have been provided by Csajb\'ok, Marino, Polverino and Zanella (2018). For any large enough odd $q$, we determine exactly which codes in $\mathcal{F}$ are MRD. We also show that the MRD codes in $\mathcal{F}$ are not equivalent to any other MRD codes known so far.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8447573816e8b8b2f52d5e42dad0e68d https://doi.org/10.1007/s10623-022-01179-0 Zobrazit plný text záznamu Full text from SpringerLink