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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

Tetsuya KOJIMA

Tokyo College

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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 -