On Trellis Structures for Reed-Muller Codes

Authors:
Tim Blackmore;Graham H. Norton
Affiliations:
Department of Electrical and Electronic Engineering, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom;Department of Electrical and Electronic Engineering, University of Bristol, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom
Venue:
Finite Fields and Their Applications
Year:
2000

Citing 11
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Abstract

We study trellises of Reed-Muller codes from first principles. Our approach to local trellis behaviour seems to be new and yields amongst other things another proof of a result of Berger and Be'ery on the state complexity of Reed-Muller codes. We give a general form of a minimal-span generator matrix for the family of Reed-Muller codes with their standard bit-order. We apply this to determining the number of parallel subtrellises in any uniform sectionalisation of a Reed-Muller code and to designing trellises for Reed-Muller codes with more parallel subtrellises than the minimal trellis, but with the same state complexity.