The minimum distance of all binary cyclic codes of odd lengths from 69 to 99

Abstract
A computer search has been made to determine the true minimum distancedfor all binary cyclic codes having odd lengthsnin the range69leq nleq 99. Using an algorithm originally developed by C. L. Chen, the generator matrixGof each(n,k)binary cyclic code was put in systematic form. All possible codewords obtained from sums ofirows ofG, fori= 1,2, cdots,upsilon, were examined, and the minimum distanced_{upsilon}of this set was recorded. Thend=d_{upsilon}wheneverupsilon >{(d_{upsilon}-l)k/n}-l. Known equivalences among cyclic codes were taken into account, and only one code from each equivalence class was listed. Letg(x)dividex^{n}-1, wherex - 1is not a factor ofg(x). Then the minimum distances of the codes generated byg(x),(x - l)g(x)and their duals are listed together. For each such set of codes, the value ofupsilonfor which a codeword of minimum weight first appeared is listed. The codes found were compared with the list of best codes tabulated by Sloane [5]. Many good cyclic codes have been found. Among the best(n,k,d)cyclic codes found are the following: (73, 27, 20), (73, 36, 16), (85, 12, 34), (85, 20, 28), (87, 31, 22), (89, 56, 11), (91, 51, 14), (93, 20, 32), (93, 23, 29), (93, 31, 24), (93, 33, 22).

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