Weight spectrum of quasi-perfect binary codes with distance 4
VB Afanassiev, AA Davydov - 2017 IEEE International …, 2017 - ieeexplore.ieee.org
VB Afanassiev, AA Davydov
2017 IEEE International Symposium on Information Theory (ISIT), 2017•ieeexplore.ieee.orgWe consider the weight spectrum of a class of quasi-perfect binary linear codes with code
distance 4. For example, extended Hamming code and Panchenko code are the known
members of this class. Also, it is known that in many cases Panchenko code has the minimal
number of weight 4 codewords. We give exact recursive formulas for the weight spectrum of
quasi-perfect codes and their dual codes. As an example of application of the weight
spectrum we derive a lower estimate for the conditional probability of correction of erasure …
distance 4. For example, extended Hamming code and Panchenko code are the known
members of this class. Also, it is known that in many cases Panchenko code has the minimal
number of weight 4 codewords. We give exact recursive formulas for the weight spectrum of
quasi-perfect codes and their dual codes. As an example of application of the weight
spectrum we derive a lower estimate for the conditional probability of correction of erasure …
We consider the weight spectrum of a class of quasi-perfect binary linear codes with code distance 4. For example, extended Hamming code and Panchenko code are the known members of this class. Also, it is known that in many cases Panchenko code has the minimal number of weight 4 codewords. We give exact recursive formulas for the weight spectrum of quasi-perfect codes and their dual codes. As an example of application of the weight spectrum we derive a lower estimate for the conditional probability of correction of erasure patterns of high weights (equal to or greater than code distance).
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