Hadamard-Type Matrices on Finite Fields and Complete Complementary Codes
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 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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.12 pp.1651-1658
- Publication Date
- 2019/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.1651
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Sequences
Authors
Tetsuya KOJIMA
Tokyo College
Keyword
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Tetsuya KOJIMA, "Hadamard-Type Matrices on Finite Fields and Complete Complementary Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 12, pp. 1651-1658, December 2019, doi: 10.1587/transfun.E102.A.1651.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1651/_p
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@ARTICLE{e102-a_12_1651,
author={Tetsuya KOJIMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Hadamard-Type Matrices on Finite Fields and Complete Complementary Codes},
year={2019},
volume={E102-A},
number={12},
pages={1651-1658},
abstract={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.},
keywords={},
doi={10.1587/transfun.E102.A.1651},
ISSN={1745-1337},
month={December},}
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TY - JOUR
TI - Hadamard-Type Matrices on Finite Fields and Complete Complementary Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1651
EP - 1658
AU - Tetsuya KOJIMA
PY - 2019
DO - 10.1587/transfun.E102.A.1651
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2019
AB - 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.
ER -
English
