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On binary cyclic codes of odd lengths from 101 to 127

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2 Author(s)
D. Schomaker ; Math. Inst., Munster Univ., Germany ; M. Wirtz

All binary cyclic codes of odd lengths are checked from 101 to 127 to find codes which are better than those in a table by T. Verhoeff (1989). There are five such cases, namely, (117, 36, 32), (117, 37, 29), (117, 42, 26), (117, 49, 24), and (127, 36 35) cyclic codes. According to Verhoeff's table the previously known ranges of the highest minimum-distance were 28-40, 28-40, 25-37, 22-32, and 32-46, respectively. Applying constructions X and Y1, (120, 37, 32) and (108, 28, 32) codes were found. Moreover, the highest minimum-distances that cyclic codes of length 127 can attain are determined.<>

Published in:

IEEE Transactions on Information Theory  (Volume:38 ,  Issue: 2 )