Error Correcting Codes Associated with Complex Hadamard Matrices

Authors

I. Heng, Old Dominion University
C. H. Cooke, Old Dominion University

Document Type

Article

Publication Date

1998

DOI

10.1016/s0893-9659(98)00059-7

Publication Title

Applied Mathematics Letters

Volume

11

Issue

4

Pages

77-80

Abstract

For primes p > 2, the generalized Hadamard matrix H(p,pt) can be expressed as H = x^A, where the notation means h_ij = x^aij. It is shown that the row vectors of A represent a p-ary error correcting code. Depending upon the value of t, either linear or nonlinear codes emerge. Code words are equidistant and have minimum Hamming distance d = (p − 1)t. The code can be extended so as to possess N = p²t code words of length pt − 1.

Comments

Elsevier open access. Copyright © 1998 Published by Elsevier Ltd. All rights reserved.

Original Publication Citation

Heng, I., & Cooke, C. H. (1998). Error correcting codes associated with complex Hadamard matrices. Applied Mathematics Letters, 11(4), 77-80. doi:10.1016/s0893-9659(98)00059-7

Repository Citation

Heng, I. and Cooke, C. H., "Error Correcting Codes Associated with Complex Hadamard Matrices" (1998). Mathematics & Statistics Faculty Publications. 130.
https://digitalcommons.odu.edu/mathstat_fac_pubs/130