Ranks and kernels of codes from generalized Hadamard matrices

Steven T. Dougherty; Josep Rifà; Mercè Villanueva

doi:10.1109/TIT.2015.2509061

Ranks and kernels of codes from generalized Hadamard matrices

Steven T. Dougherty, Josep Rifà, Mercè Villanueva

Research output: Contribution to journal › Article › Research › peer-review

12 Citations (Scopus)

Abstract

© 2015 IEEE. The ranks and kernels of generalized Hadamard matrices are studied. It is proved that any generalized Hadamard matrix H(q,λ) over Fq, q > 3, or q = 3 and gcd(3, λ) = 1, generates a self-orthogonal code. This result puts a natural upper bound on the rank of the generalized Hadamard matrices. Lower and upper bounds are given for the dimension of the kernel of the corresponding generalized Hadamard codes. For specific ranks and dimensions of the kernel within these bounds, generalized Hadamard codes are constructed.

Original language	English
Article number	7362191
Pages (from-to)	687-694
Journal	IEEE Transactions on Information Theory
Volume	62
DOIs	https://doi.org/10.1109/TIT.2015.2509061
Publication status	Published - 1 Feb 2016

Keywords

Generalized Hadamard code
Generalized Hadamard matrix
Kernel
Nonlinear code
Rank
Self-orthogonal code

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10.1109/TIT.2015.2509061

https://ddd.uab.cat/record/145233

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title = "Ranks and kernels of codes from generalized Hadamard matrices",

abstract = "{\textcopyright} 2015 IEEE. The ranks and kernels of generalized Hadamard matrices are studied. It is proved that any generalized Hadamard matrix H(q,λ) over Fq, q > 3, or q = 3 and gcd(3, λ) = 1, generates a self-orthogonal code. This result puts a natural upper bound on the rank of the generalized Hadamard matrices. Lower and upper bounds are given for the dimension of the kernel of the corresponding generalized Hadamard codes. For specific ranks and dimensions of the kernel within these bounds, generalized Hadamard codes are constructed.",

keywords = "Generalized Hadamard code, Generalized Hadamard matrix, Kernel, Nonlinear code, Rank, Self-orthogonal code",

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doi = "10.1109/TIT.2015.2509061",

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T1 - Ranks and kernels of codes from generalized Hadamard matrices

AU - Dougherty, Steven T.

AU - Rifà, Josep

AU - Villanueva, Mercè

PY - 2016/2/1

Y1 - 2016/2/1

N2 - © 2015 IEEE. The ranks and kernels of generalized Hadamard matrices are studied. It is proved that any generalized Hadamard matrix H(q,λ) over Fq, q > 3, or q = 3 and gcd(3, λ) = 1, generates a self-orthogonal code. This result puts a natural upper bound on the rank of the generalized Hadamard matrices. Lower and upper bounds are given for the dimension of the kernel of the corresponding generalized Hadamard codes. For specific ranks and dimensions of the kernel within these bounds, generalized Hadamard codes are constructed.

AB - © 2015 IEEE. The ranks and kernels of generalized Hadamard matrices are studied. It is proved that any generalized Hadamard matrix H(q,λ) over Fq, q > 3, or q = 3 and gcd(3, λ) = 1, generates a self-orthogonal code. This result puts a natural upper bound on the rank of the generalized Hadamard matrices. Lower and upper bounds are given for the dimension of the kernel of the corresponding generalized Hadamard codes. For specific ranks and dimensions of the kernel within these bounds, generalized Hadamard codes are constructed.

KW - Generalized Hadamard code

KW - Generalized Hadamard matrix

KW - Kernel

KW - Nonlinear code

KW - Rank

KW - Self-orthogonal code

U2 - 10.1109/TIT.2015.2509061

DO - 10.1109/TIT.2015.2509061

M3 - Article

SN - 0018-9448

VL - 62

SP - 687

EP - 694

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

M1 - 7362191

ER -

Ranks and kernels of codes from generalized Hadamard matrices

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Keywords

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