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In this paper, we show a manner to use properties of the permutation group on some binary linear codes to improve the decoding algorithms. We search especially for particular permutations and we prove bounds on dimension of a special subcode of the idempotent sub-code. This σ-subcode can have very lower dimension in practice than the original code. We give(More)
In this paper we construct new subcodes of the second-order binary Reed-Muller code by using the permutation group and by projecting the code onto codes with smaller parameters. The permutation group of Reed-Muller codes is the general affine group and can be decomposed into the semi-direct product of the translation group and the general linear group. The(More)
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