The Preparata and Goethals codes: trellis complexity and twisted squaring constructions

Author

Shany, Yaron ; Ery, Yair Be

Author_Institution

Dept. of Electr. Eng., Tel Aviv Univ., Israel

Volume

45

Issue

5

fYear

1999

fDate

7/1/1999 12:00:00 AM

Firstpage

1667

Lastpage

1673

Abstract

The trellis complexity of the Preparata and Goethals codes is examined. It is shown that at least for a given set of permutations these codes are rectangular. Upper bounds on the state complexity profiles of the Preparata and Goethals codes are given. The upper bounds on the state complexity of the Preparata and Goethals codes are determined by the dimension/length profiles (DLP) of the extended primitive double- and triple-error-correcting BCH codes, respectively. A twisted squaring construction for the Preparata and Goethals codes is given, based on the double- and triple-error-correcting extended primitive BCH codes, respectively

Keywords

BCH codes; binary codes; block codes; error correction codes; nonlinear codes; trellis codes; Goethals codes; Preparata codes; binary nonlinear codes; block codes; dimension/length profiles; double-error-correcting BCH codes; extended primitive BCH codes; rectangular codes; state complexity; trellis complexity; triple-error-correcting BCH codes; twisted squaring constructions; upper bounds; Binary codes; Block codes; Decoding; Information theory; Linear code; Upper bound; Viterbi algorithm;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.771240

Filename

771240