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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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초록· 키워드
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It is well-known that there exists a constant-weight $[s \theta_{k-1},k, $ $ sq^{k-1}]_q$ code for any positive integer $s$, which is an $s$-fold simplex code, where $\theta_{j}=(q^{j+1}-1)/(q-1)$. This gives an upper bound $n_q(k, s q^{k-1}+d) \le s \theta_{k-1} + n_q(k,d)$ for any positive integer $d$, where $n_q(k,d)$ is the minimum length $n$ for which an $[n,k,d]_q$ code exists. We construct a two-weight $[s \theta_{k-1}+1,k, s q^{k-1}]_q$ code for $1 \le s \le k-3$, which gives a better upper bound $n_q(k, s q^{k-1}+d) \le s \theta_{k-1} +1 + n_q(k-1,d)$ for $1 \le d \le q^s$. As another application, we prove that $n_q(5,d)=\sum_{i=0}^{4}{\left\lceil{{d}/{q^i}}\right\rceil}$ for $q^{4}+1 \le d \le q^4+q$ for any prime power $q$.
목차
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참고문헌 (10)
참고문헌 신청
F. J. MacWilliams / 1977 / The Theory of Error-Correcting Codes / North-Holland
G. Solomon / 1965 / Algebraically punctured cyclic codes / Inform. and Control 8 (2) : 170 ~ 179
J. H. Griesmer / 1960 / A bound for error-correcting codes / IBM J. Res. Develop 4 : 532 ~ 542
J. W. P. Hirschfeld / 1998 / Projective Geometries over Finite Fields / Clarendon Press
R. Calderbank / 1986 / The geometry of two-weight codes / Bull. London Math. Soc 18 (2) : 97 ~ 122
G. Solomon / 1965 / Algebraically punctured cyclic codes / Inform. and Control 8 (2) : 170 ~ 179
J. H. Griesmer / 1960 / A bound for error-correcting codes / IBM J. Res. Develop 4 : 532 ~ 542
J. W. P. Hirschfeld / 1998 / Projective Geometries over Finite Fields / Clarendon Press
R. Calderbank / 1986 / The geometry of two-weight codes / Bull. London Math. Soc 18 (2) : 97 ~ 122
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