Abstract
Binary block codes for correcting asymmetric errors are called binary AsEC block codes. With the properties of perfect codes for the binary symmetric channel in mind, natural definitions of perfect, weakly perfect and uniformly weakly perfect binary AsEC block codes are given and their properties are studied.
It is shown that a perfect asymmetric-error-correcting code is trivial or is equal to the repetition code. Also, it is proved that any weakly perfect code which is nontrivial can always be enlarged to a bigger code of the same length and the same distance. As necessary ingredients for the proofs of those two results, several related properties of codes for correcting asymmetric errors are studied as well.
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© 1993 Springer-Verlag Berlin Heidelberg
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Fang, G., van Tilborg, H.C.A., Sun, F.W., Honkala, I.S. (1993). Some features of binary block codes for correcting asymmetric errors. In: Cohen, G., Mora, T., Moreno, O. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1993. Lecture Notes in Computer Science, vol 673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56686-4_37
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DOI: https://doi.org/10.1007/3-540-56686-4_37
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