On the Pless-construction and ML decoding of the (48,24,12) quadratic residue code

Author

Esmaeili, Morteza ; Gulliver, T. Aaron ; Khandani, Amir K.

Author_Institution

Dept. of Math. Sci., Isfahan Univ. of Technol., Iran

Volume

49

Issue

6

fYear

2003

fDate

6/1/2003 12:00:00 AM

Firstpage

1527

Lastpage

1535

Abstract

We present a method for maximum likelihood decoding of the (48,24,12) quadratic residue code. This method is based on projecting the code onto a subcode with an acyclic Tanner graph, and representing the set of coset leaders by a trellis diagram. This results in a two level coset decoding which can be considered a systematic generalization of the Wagner rule. We show that unlike the (24,12,8) Golay code, the (48,24,12) code does not have a Pless-construction which has been an open question in the literature. It is determined that the highest minimum distance of a (48,24) binary code having a Pless (1986) construction is 10, and up to equivalence there are three such codes.

Keywords

Golay codes; binary codes; graph theory; linear codes; maximum likelihood decoding; residue codes; Golay code; Hamming codes; ML decoding; Pless based code construction; Reed-Muller codes; Wagner rule; acyclic Tanner graph; binary code; coset leaders; error-correcting codes; extended Golay codes; hexacode; linear block code; maximum likelihood decoding; minimum code distance; quadratic residue code; subcode; trellis diagram; two-level coset decoding; Binary codes; Block codes; Communication systems; Convolutional codes; Error correction codes; Maximum likelihood decoding; Viterbi algorithm;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2003.811930

Filename

1201075