CONSTANT weight codes are very important in coding theory for its application to communication. In refs. [1—5], the undetected error probabilities (UEP)of binary nonlinear constant weight codes (BNCW) were studied, a...CONSTANT weight codes are very important in coding theory for its application to communication. In refs. [1—5], the undetected error probabilities (UEP)of binary nonlinear constant weight codes (BNCW) were studied, and Wang et al. showed that when n】8, BNCW codes (n, 2, ω) were not proper, Wang proposed a conjecture that when n】4δ and δ】 1, BNCW codes (n, 2δ, ω) are not proper. in this note, the error-detecting abilities展开更多
A new construction of constant-composition codes based on all known perfect nonlinear functions from Fqm to itself is presented, which provides a kind of unified constructions of constant-composition codes based on al...A new construction of constant-composition codes based on all known perfect nonlinear functions from Fqm to itself is presented, which provides a kind of unified constructions of constant-composition codes based on all known perfect nonlinear functions from F qm to itself.It is proved that the new constant-composition codes are optimal with respect to the Luo-Fu-Vinck-Chen bound, when m is an odd positive integer greater than 1.Finally, we point out that two constructions of constant-composition codes, proposed by Ding Cunsheng et al.in 2005, are equivalent to two special types of the new constant-composition codes.展开更多
文摘CONSTANT weight codes are very important in coding theory for its application to communication. In refs. [1—5], the undetected error probabilities (UEP)of binary nonlinear constant weight codes (BNCW) were studied, and Wang et al. showed that when n】8, BNCW codes (n, 2, ω) were not proper, Wang proposed a conjecture that when n】4δ and δ】 1, BNCW codes (n, 2δ, ω) are not proper. in this note, the error-detecting abilities
基金Supported in part by the National Natural Science Foundation of China (Grant Nos 60573028, 60803156)the Open Research Fund of the National Mobile Communications Research Laboratory of Southeast University (Grant No W200805)in part by Singapore Ministry of Education Academic Research Fund (Grant No T206B2204)
文摘A new construction of constant-composition codes based on all known perfect nonlinear functions from Fqm to itself is presented, which provides a kind of unified constructions of constant-composition codes based on all known perfect nonlinear functions from F qm to itself.It is proved that the new constant-composition codes are optimal with respect to the Luo-Fu-Vinck-Chen bound, when m is an odd positive integer greater than 1.Finally, we point out that two constructions of constant-composition codes, proposed by Ding Cunsheng et al.in 2005, are equivalent to two special types of the new constant-composition codes.
