Optimum shortened cyclic codes for burst-error correction
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TL;DR
The construction of the most efficient shortened cyclic (pseudo-cyclic) codes that can correct every burst-error of length b or less, which have the maximum number of information digits k among all shortenedcyclic burst- b codes with a given number of check digits r.
Abstract
This paper is concerned with the construction of the most efficient shortened cyclic (pseudo-cyclic) codes that can correct every burst-error of length b or less. These codes have the maximum number of information digits k among all shortened cyclic burst- b codes with a given number of check digits r . The search procedure described is readily programmable for computer execution and efficient particularly for the case where r is close to the theoretical minimum of 2b check digits. For 2 \leq b \leq 10 , several optimum shortened cyclic codes in the above-mentioned sense have been found. Their code-lengths and generators are tabulated in this paper.