[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2013.26.1.147

DETERMINATION OF MINIMUM LENGTH OF SOME LINEAR CODES

Cheon, Eun Ju (Department of Mathematics and RINS Gyeongsang National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.26, no.1, 2013 , pp. 147-159 More about this Journal

Abstract

Hamada ([8]) and Maruta ([17]) proved the minimum length $n_3(6,\;d)=g_3(6,\;d)+1$ for some ternary codes. In this paper we consider such minimum length problem for $q{\geq}4$ , and we prove that $n_q(6,\;d)=g_q(6,\;d)+1$ for $d=q^5-q^3-q^2-2q+e$ , $1{\leq}e{\leq}q$ . Combining this result with Theorem A in [4], we have $n_q(6,\;d)=g-q(6,\;d)+1$ for $q^5-q^3-q^2-2q+1{\leq}d{\leq}q^5-q^3-q^2$ with $q{\geq}4$ . Note that $n_q(6,\;d)=g_q(6,\;d)$ for $q^5-q^3-q^2+1{\leq}d{\leq}q^5$ by Theorem 1.2.

Keywords

linear code; minimum length; Griesmer bound; minihyper; projective space;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

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