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http://dx.doi.org/10.4134/BKMS.2008.45.3.419

ON THE MINIMUM LENGTH OF SOME LINEAR CODES OF DIMENSION 6  

Cheon, Eun-Ju (DEPARTMENT OF MATHEMATICS AND RINS GYEONGSANG NATIONAL UNIVERSITY)
Kato, Takao (DEPARTMENT OF MATHEMATICAL SCIENCES YAMAGUCHI UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.3, 2008 , pp. 419-425 More about this Journal
Abstract
For $q^5-q^3-q^2-q+1{\leq}d{\leq}q^5-q^3-q^2$, we prove the non-existence of a $[g_q(6,d),6,d]_q$ code and we give a $[g_q(6,d)+1,6,d]_q$ code by constructing appropriate 0-cycle in the projective space, where $g_q (k,d)={{\sum}^{k-1}_{i=0}}{\lceil}\frac{d}{q^i}{\rceil}$. Consequently, we have the minimum length $n_q(6,d)=g_q(6,d)+1\;for\;q^5-q^3-q^2-q+1{\leq}d{\leq}q^5-q^3-q^2\;and\;q{\geq}3$.
Keywords
Griesmer bound; linear code; 0-cycle; minimum length; projective space;
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  • Reference
1 T. Maruta, On the nonexistence of q-ary linear codes of dimension five, Des. Codes Cryptogr. 22 (2001), no. 2, 165-177   DOI
2 T. Maruta, Griesmer bound for linear codes over finite fields, Available: http://www. geocities.com/mars39.geo/griesmer.htm
3 N. Hamada and T. Helleseth, The nonexistence of some ternary linear codes and update of the bounds for n3(6, d), 1 $\leq$ d $\leq$ 243, Math. Japon. 52 (2000), no. 1, 31-43
4 R. Hill, Optimal linear codes, Cryptography and coding, II (Cirencester, 1989), 75-104, Inst. Math. Appl. Conf. Ser. New Ser., 33, Oxford Univ. Press, New York, 1992
5 N. Hamada, A characterization of some n, k, d; q-codes meeting the Griesmer bound using a minihyper in a finite projective geometry, Discrete Math. 116 (1993), no. 1-3, 229-268   DOI   ScienceOn