논문KCI 등재
On the minimum length of some linear codes of dimension 6
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초록
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.
Abstract
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.
참고문헌 (5)
- -codes meeting the Griesmer bound using a minihyper in a finite projective geometry, "Discrete Mathematics", 1993, 229~268
- N. Hamada, "The nonexistence of some ternary linear codes and update of the bounds for n3(6, d), 1 ≤ d ≤ 243", Mathematica Japonica, 52(1), pp.31~43 (2000)
- R. Hill, "Optimal linear codes, Cryptography and coding, II (Cirencester, 1989)", Institute of Mathematics and its Applications Conference Series New Series, 33, pp.75~104 (1992)
- T. Maruta, "On the nonexistence of q-ary linear codes of dimension five", Designs codes and cryptography, 22(2), pp.165~177 (2001)
- "Griesmer bound for linear codes over finite fields"[URL]
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