Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Polynomial Construction Of Complex Hadamard Matrices With Cyclic Core, C. H. Cooke, I. Heng
Polynomial Construction Of Complex Hadamard Matrices With Cyclic Core, C. H. Cooke, I. Heng
Mathematics & Statistics Faculty Publications
Conditions are given which are necessary and sufficient to ensure invariance of an M-sequence under periodic rearrangement. In conjunction with a certain uniformity property of polynomial coefficients, these conditions yield a simple method by which complex Hadamard matrices with cyclic core can be constructed. In such cases, a real p-ary linear cyclic error correcting code may be associated with the complex Hadamard matrix.
Error Correcting Codes Associated With Complex Hadamard Matrices, I. Heng, C. H. Cooke
Error Correcting Codes Associated With Complex Hadamard Matrices, I. Heng, C. H. Cooke
Mathematics & Statistics Faculty Publications
For primes p > 2, the generalized Hadamard matrix H(p,pt) can be expressed as H = xA, where the notation means hij = xaij. 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 …