On the Optimum Cyclic Subcode Chains of $\mathcal{RM}(2,m)^*$ for Increasing Message Length
نویسندگان
چکیده
The distance profiles of linear block codes can be employed to design variational coding scheme for encoding message with variational length and getting lower decoding error probability by large minimum Hamming distance. Considering convenience for encoding, we focus on the distance profiles with respect to cyclic subcode chains (DPCs) of cyclic codes over GF (q) with length n such that gcd(n, q) = 1. In this paper the optimum DPCs and the corresponding optimum cyclic subcode chains are investigated on the punctured second-order ReedMuller code RM(2, m)∗ for increasing message length, where two standards on the optimums are studied according to the rhythm of increase.
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On the bounds and achievability about the ODPC of $\mathcal{GRM}(2, m)^*$ over prime field for increasing message length
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