Summary
The 2018 International Symposium on Information Theory and Its Applications (ISITA2018)
2018
Session Number:Tu-PM-2-4
Session:
Number:Tu-PM-2-4.2
Hadamard-type Matrices on Finite Fields and Their Applications to Sequence Generation
Tetsuya Kojima,
pp.481-485
Publication Date:2018/10/18
Online ISSN:2188-5079
DOI:10.34385/proc.55.Tu-PM-2-4.2
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Summary:
Hadamard matrix is defined as a square matrix where any components are -1 or +1, and where any pairs of rows are mutually orthogonal. In this study, we consider the similar matrix on finite field GF(p) where p is an odd prime. In such a matrix, every component is one of the integers on GF(p)＼{0}, that is, ｛1, 2,・・・, p - 1}. Any additions and multiplications should be executed under modulo p. In this paper, a method to generate such matrices is proposed. In addition, the paper includes the applications to generate n-shift orthogonal sequences and complete complementary codes. The generated complete complementary code is a family of multivalued sequences on GF(p), where the number of sequence sets, the number of sequences in each sequence set and the sequence length depend on the various divisors of p - 1. Such complete complementary codes with various parameters have not been proposed in previous studies.