A non-cyclic triple-error-correcting BCH-like code and some minimum distance results |
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| Authors: | Carl Bracken Faruk Göloğlu |
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| Institution: | 1. Department of Mathematics, School of Physical & Mathematical Sciences, Nanyang Technology University, Singapore, Singapore
2. School of Mathematical Sciences, University College Dublin, Dublin, Ireland
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| Abstract: | In this paper, we give the first example of a non-cyclic triple-error-correcting code which is not equivalent to the primitive BCH code. It has parameters 63, 45, 7]. We also give better bounds on minimum distances of some 2 n ? 1, 2 n - 3n - 1] cyclic codes with three small zeroes. Finally, we reprove weight distribution results of Kasami for triple-error-correcting BCH-like codes using direct methods. |
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