The split weight (wL, wR) enumeration of Reed-Muller codes for wL+wR<2dmin
Formulas for the distributions of split weights (w L , w R ) of Reed-Muller codes are presented for w L +w r less than twice the minimum weight dmin. A canonical form for all the relevant Boolean polynomials is derived. These results are applied to analyzing the structure and complexity of subtrellises of codewords of weights less than 2dmin of Reed-Muller codes.
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