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This article is cited in 5 scientific papers (total in 5 papers)
Linear recursive MDS-codes of dimensions 2 and 3
A. S. Abashin
Abstract:
A code $\mathcal K$ of length $n$ in an alphabet $\Omega$ is called linear in the general sense or simply linear if there exists a binary operation $+$ on $\Omega$ such that $(\Omega,+)$ is an abelian group and
$\mathcal K$ is a subgroup of $(\Omega^n,+)$. We say that $\mathcal K$ is a $k$-recursive code if
$\mathcal K$ consists of all words of length $n\ge k$ such that their coordinates are obtained from the first $k$ coordinates by some fixed recursive rule.
Let $l^r(k,q)$ be the maximal $n$ such that there exists a linear $k$-recursive code of length $n$ in an alphabet of $q$ elements with the distance $n-k+1$ (an MDS code), and let $l^{ir}(k,q)$ be the
maximal $n$ such that there exists a linear $k$-recursive idempotent (containing all constant words) MDS code of length $n$ in an alphabet of $q$ elements. Using the theory of linear recurring sequences we find $l^{ir}(2,q)$ and $l^{r}(3,q)$ for primary $q$.
Received: 12.10.1999
Citation:
A. S. Abashin, “Linear recursive MDS-codes of dimensions 2 and 3”, Diskr. Mat., 12:2 (2000), 140–153; Discrete Math. Appl., 10:3 (2000), 319–332
Linking options:
https://www.mathnet.ru/eng/dm325https://doi.org/10.4213/dm325 https://www.mathnet.ru/eng/dm/v12/i2/p140
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