On Optimal Linear Codes over ${\mathbb{F}}_8$

Autor:	Rie Kanazawa, Tatsuya Maruta
Rok vydání:	2011
Předmět:	Combinatorics Continuation Code (set theory) Computational Theory and Mathematics Integer Applied Mathematics Discrete Mathematics and Combinatorics Geometry and Topology Extension (predicate logic) Upper and lower bounds Theoretical Computer Science Mathematics
Zdroj:	The Electronic Journal of Combinatorics. 18
ISSN:	1077-8926
DOI:	10.37236/521
Popis:	Let $n_q(k,d)$ be the smallest integer $n$ for which there exists an $[n,k,d]_q$ code for given $q,k,d$. It is known that $n_8(4,d) = \sum_{i=0}^{3} \left\lceil d/8^i \right\rceil$ for all $d \ge 833$. As a continuation of Jones et al. [Electronic J. Combinatorics 13 (2006), #R43], we determine $n_8(4,d)$ for 117 values of $d$ with $113 \le d \le 832$ and give upper and lower bounds on $n_8(4,d)$ for other $d$ using geometric methods and some extension theorems for linear codes.
Databáze:	OpenAIRE
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