Algorithms for q-ary error-correcting codes with limited magnitude and feedback
نویسندگان
چکیده
منابع مشابه
Optimal, systematic, q-ary codes correcting all asymmetric and symmetric errors of limited magnitude
Systematic -ary ( ) codes capable of correcting all asymmetric errors of maximum magnitude , where , are given. These codes are shown to be optimal. Further, simple encoding/decoding algorithms are described. The proposed code can be modified to design codes correcting all symmetric errors of maximum magnitude , where .
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We consider codes over the alphabet Q = {0, 1,. .. , q − 1} intended for the control of unidirectional errors of level ℓ. That is, the transmission channel is such that the received word cannot contain both a component larger than the transmitted one and a component smaller than the transmitted one. Moreover, the absolute value of the difference between a transmitted component and its received ...
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The expression for ω 2,2,r (2t) in Theorem 9 is misprinted in the original publication of this article. It should have been the same as for ω 2,1,r (2t) in Theorem 11. The correct expression in Theorem 9 will be Theorem 9 For q = 2t where t is odd, we have ω 2,2,r (2t) = 1 2 (2 r − 1)(t r + 1) .
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The concepts of a linear covering code and a covering set for the limitedmagnitude-error channel are introduced. A number of covering-set constructions, as well as some bounds, are given. In particular, optimal constructions are given for some cases involving small-magnitude errors. A problem of Stein is partially solved for these cases. Optimal packing sets and the corresponding error-correcti...
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The maximum possible number of codewords in a q-ary code of length n and minimum distance d is denoted Aq(n,d). It is a fundamental problem in coding theory to determine this value for given parameters q, n and d. Codes that attain the maximum are said to be optimal. Unfortunately, for many different values of these parameters, the maximum number of codewords is currently unknown: instead we ha...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2021
ISSN: 0012-365X
DOI: 10.1016/j.disc.2020.112199