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- W1600887176 abstract "We say that an s-subset of codewords of a binary code X is s L -bad in X if there exists an L-subset of other codewords in X whose disjunctive sum is covered by the disjunctive sum of the given s codewords. Otherwise, this s-subset of codewords is said to be s L -good in X. A binary code X is said to be a list-decoding disjunctive code of strength s and list size L (an s L -LD code) if it does not contain s L -bad subsets of codewords. We consider a probabilistic generalization of s L -LD codes; namely, we say that a code X is an almost disjunctive s L -LD code if the fraction of s L -good subsets of codewords in X is close to 1. Using the random coding method on the ensemble of binary constant-weight codes, we establish lower bounds on the capacity and error exponent of almost disjunctive s L -LD codes. For this ensemble, the obtained lower bounds are tight and show that the capacity of almost disjunctive s L -LD codes is greater than the zero-error capacity of disjunctive s L -LD codes." @default.
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- W1600887176 date "2015-04-01" @default.
- W1600887176 modified "2023-10-18" @default.
- W1600887176 title "Almost disjunctive list-decoding codes" @default.
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- W1600887176 doi "https://doi.org/10.1134/s0032946015020039" @default.
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