Hadamard-Type Matrices on Finite Fields and Complete Complementary Codes

• KOJIMA Tetsuya

  Department of Computer Science, National Institute of Technology, Tokyo College

抄録

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 work, 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 multi-valued sequences on GF(p)\{0}, 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.

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E102.A (12), 1651-1658, 2019-12-01

  一般社団法人 電子情報通信学会

キーワード

• Hadamard-type matrix
• finite field
• cyclic group
• multiplicative inverse
• complete complementary code

詳細情報

• CRID: 1390564227352353536
• NII論文ID: 130007754022
• DOI: 10.1587/transfun.e102.a.1651
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E102.A/12/E102.A_1651/_pdf
• 本文言語コード: en
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