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For q5-q³-q²-q+1≤ d ≤ q5-q³-q², we prove the non-existence of a [gq(6,d),6,d]q code and we give a [gq(6,d) +1, 6, d]q code by constructing appropriate 0-cycle in the projective space, where [수식]. Consequently, we have the minimum length nq(6,d)=gq(6,d) +1 for q5-q³-q²-q+1 ≤ d ≤ q5 -q³ -q² and q ≤ 3.
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참고문헌 (5)
참고문헌 신청
N. Hamada / 1993 / A characterization of some [n, k, d q]-codes meeting the Griesmer bound using a minihyper in a finite projective geometry / Discrete Mathematics 116 (1) :
N. Hamada / 2000 / The nonexistence of some ternary linear codes and update of the bounds for n3(6, d), 1 ≤ d ≤ 243 / Mathematica Japonica 52 (1) : 31 ~ 43
R. Hill / 1992 / Optimal linear codes, Cryptography and coding, II (Cirencester, 1989) / Institute of Mathematics and its Applications Conference Series New Series 33 : 75 ~
T. Maruta / / Griesmer bound for linear codes over finite fields
T. Maruta / 2001 / On the nonexistence of q-ary linear codes of dimension five / Designs codes and cryptography 22 (2) : 165 ~ 177
N. Hamada / 2000 / The nonexistence of some ternary linear codes and update of the bounds for n3(6, d), 1 ≤ d ≤ 243 / Mathematica Japonica 52 (1) : 31 ~ 43
R. Hill / 1992 / Optimal linear codes, Cryptography and coding, II (Cirencester, 1989) / Institute of Mathematics and its Applications Conference Series New Series 33 : 75 ~
T. Maruta / / Griesmer bound for linear codes over finite fields
T. Maruta / 2001 / On the nonexistence of q-ary linear codes of dimension five / Designs codes and cryptography 22 (2) : 165 ~ 177
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