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On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes

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4 Author(s)
Kasami, T. ; Dept. of Inf. & Comput. Sci., Osaka Univ., Japan ; Takata, T. ; Fujiwara, T. ; Shu Lin

It was shown earlier that for a punctured Reed-Muller (RM) code or a primitive BCH code, which contains a punctured RM code of the same minimum distance as a large subcode, the state complexity of the minimal trellis diagrams is much greater than that for an equivalent code obtained by a proper permutation of the bit positions. The problem of finding a permutation of the bit positions for a given code that minimizes the state complexity of its minimal trellis diagram is related to the generalized Hamming weight hierarchy of a code, and it is shown that, for RM codes, the standard binary order of bit positions is optimum at every bit position with respect to the state complexity of a minimal trellis diagram by using a theorem due to V.K. Wei (1991). The state complexity of the trellis diagram for the extended and permuted (64, 24) BCH code is discussed

Published in:

Information Theory, IEEE Transactions on  (Volume:39 ,  Issue: 1 )

Date of Publication:

Jan 1993

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