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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</tex> or less. These codes have the maximum number of information digits <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> among all shortened cyclic burst- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</tex> codes with a given number of check digits <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> . The search procedure described is readily programmable for computer execution and efficient particularly for the case where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> is close to the theoretical minimum of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2b</tex> check digits. For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 \leq b \leq 10</tex> , several optimum shortened cyclic codes in the above-mentioned sense have been found. Their code-lengths and generators are tabulated in this paper.
Published Version
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