ON THE MINIMUM LENGTH OF SOME LINEAR CODES OF DIMENSION 6

Title & Authors
ON THE MINIMUM LENGTH OF SOME LINEAR CODES OF DIMENSION 6
Cheon, Eun-Ju; Kato, Takao;

Abstract
For $\small{q^5-q^3-q^2-q+1{\leq}d{\leq}q^5-q^3-q^2}$, we prove the non-existence of a $\small{[g_q(6,d),6,d]_q}$ code and we give a $\small{[g_q(6,d)+1,6,d]_q}$ code by constructing appropriate 0-cycle in the projective space, where $g_q (k,d) Keywords Griesmer bound;linear code;0-cycle;minimum length;projective space; Language English Cited by 1. SOFT WS-ALGEBRAS,;;; 대한수학회논문집, 2008. vol.23. 3, pp.313-324 2. DETERMINATION OF MINIMUM LENGTH OF SOME LINEAR CODES,; 충청수학회지, 2013. vol.26. 1, pp.147-159 1. DETERMINATION OF MINIMUM LENGTH OF SOME LINEAR CODES, Journal of the Chungcheong Mathematical Society, 2013, 26, 1, 147 References 1. N. Hamada, A characterization of some n, k, d; q-codes meeting the Griesmer bound using a minihyper in a finite projective geometry, Discrete Math. 116 (1993), no. 1-3, 229-268 2. N. Hamada and T. Helleseth, The nonexistence of some ternary linear codes and update of the bounds for n3(6, d), 1$\leq$d$\leq\$ 243, Math. Japon. 52 (2000), no. 1, 31-43

3.
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

4.
T. Maruta, On the nonexistence of q-ary linear codes of dimension five, Des. Codes Cryptogr. 22 (2001), no. 2, 165-177

5.
T. Maruta, Griesmer bound for linear codes over finite fields, Available: http://www. geocities.com/mars39.geo/griesmer.htm