On complexity of trellis structure of linear block codes
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Cites background from "On complexity of trellis structure ..."
...A partial bibliography of earlier related work would include: 1) Convolutional codes and linear systems: [ 11-[SI; 2) Trellis structure of linear codes: [9]-[ 12 ]; 3) Euclidean-space codes based on group structure:...
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252 citations
References
10,083 citations
"On complexity of trellis structure ..." refers background in this paper
...5) and the property of Mattson-Solomon polynomial [5, 7]....
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...There is a permutation lr on the bit positions (see section 4) such that _r[C'] = RMm,,, the r-th order (noncyclic) Reed-Muller code of length 2" [5, 7]....
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...For 0 <_ r _< m, the r-th order (noncyclic) Reed-Muller code of length 2r_ [5, 7], denoted RM"`,,, is defined as {b(f) : f E P_,}, this is, P[RM"`,,] = P_....
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...Then C' is a subcode of C and consists of the set of all binary n-tuples represented by boolean polynomials of degree 2 or less [7]....
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...Then C' is a subcode of C and consists of the set of all binary n-tuples represented by boolean polynomials of degree 3 or less [7]....
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3,848 citations
"On complexity of trellis structure ..." refers background in this paper
...The binary primitive BCH code of length 2" - 1 and minimum Hamming distance 2"-' - 1 contains the cyclic r-th order Reed-Muller code of length 2" - 1 as a subcode [5, 6], and the dual code of the even weight subcode of the binary primitive BCH code of length 2" - 1 and a specific designed distance, denoted q(m, r), contains the cyclic r-th order Reed-Muller code of length 2" - 1 as a subcode for q(m, r) = 5, q(m, 2) = 2 tin/2/ + 3, ....
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...Let c-RMm,, denote the cyclic r-th order Reed-Muller code of length 2"* - 1 [5, 6]....
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770 citations
Additional excerpts
...Our study is motivated by the works of Wolf [1] and Forney [2] [3], especially Forney's latest work [3] in which he presented a trellis construction for linear block codes and asserted that the construction results in minimal trellises in the sense of number of states....
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...Our study is motivated by the works of Wolf [1] and Forney [2, 3], especially Forney's latest work [3] in which he presented a trellis construction for linear block codes and asserted that the construction results in minimal trellises in the sense of number of states....
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...I = 2 (2.11) This was first given by Forney [3, Appendix A]....
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709 citations
"On complexity of trellis structure ..." refers background or methods in this paper
...For a binary N-tuple v, the support of v, denoted s(v), is defined as the set of indices of bit positions where the components of v are nonzero [ 7 ]....
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...antilexicographi cal order defined by XI 7 ]....
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...However, in [II], we relate this permutation problem to the generalized Hamming weight hierarchy of a code, and we show that [or Reed-Muller codes, the standard binary order of bit positions is optimum at every bit positions with respect to the state complexity of the minimal trellis diagram by using a theorem due to Wei [ 7 ]....
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