Title :
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
fDate :
7/1/1999 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on
