New 5-dimensional linear codes over \(\mathbb{F}_5\). (English) Zbl 1433.94121

Kageyama, Yuuki; Maruta, Tatsuya

Optimal codes and related topics, OC 2013. Proceedings of the seventh international workshop, Albena, Bulgaria, September 6–12, 2013. Dedicated to Stefan Dodunekov (1945–2012). Sofia: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. 107-112 (2013).

Summary: We construct a lot of new \([n,5,d]_5\) codes to determine the exact value of \(n_5(5,d)\) or to improve the known upper bound on \(n_5(5,d)\), where \(n_q(k,d)\) is the minimum length \(n\) for which an \([n,k,d]_q\) code exists.
For the entire collection see [Zbl 1321.00113].

MSC:

94B05	Linear codes, general
11T71	Algebraic coding theory; cryptography (number-theoretic aspects)