Kernels and p-kernels of pr -ary 1-perfect codes

K. T. Phelps; J. Rifà; M. Villanueva

doi:https://doi.org/10.1007/s10623-004-3989-x

Kernels and p-kernels of pr -ary 1-perfect codes

K. T. Phelps, J. Rifà, M. Villanueva

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

13 Citations (Scopus)

Abstract

The rank of a q-ary code C is the dimension of the subspace spanned by C. The kernel of a q-ary code C of length n can be defined as the set of all translations leaving C invariant. Some relations between the rank and the dimension of the kernel of q-ary 1-perfect codes, over script F signq = GF(q) as well as over the prime field script F signp, are established. Q-ary 1-perfect codes of length n=(q m - 1)/(q - 1) with different kernel dimensions using switching constructions are constructed and some upper and lower bounds for the dimension of the kernel, once the rank is given, are established. © 2005 Springer Science+Business Media, Inc.

Original language	English
Pages (from-to)	243-261
Journal	Designs, Codes, and Cryptography
Volume	37
DOIs	https://doi.org/10.1007/s10623-004-3989-x
Publication status	Published - 1 Nov 2005

Keywords

Kernel
Nonlinear codes
Perfect codes
Rank
q-ary codes

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https://doi.org/10.1007/s10623-004-3989-x

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title = "Kernels and p-kernels of pr -ary 1-perfect codes",

abstract = "The rank of a q-ary code C is the dimension of the subspace spanned by C. The kernel of a q-ary code C of length n can be defined as the set of all translations leaving C invariant. Some relations between the rank and the dimension of the kernel of q-ary 1-perfect codes, over script F signq = GF(q) as well as over the prime field script F signp, are established. Q-ary 1-perfect codes of length n=(q m - 1)/(q - 1) with different kernel dimensions using switching constructions are constructed and some upper and lower bounds for the dimension of the kernel, once the rank is given, are established. {\textcopyright} 2005 Springer Science+Business Media, Inc.",

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TY - JOUR

T1 - Kernels and p-kernels of pr -ary 1-perfect codes

AU - Phelps, K. T.

AU - Rifà, J.

AU - Villanueva, M.

PY - 2005/11/1

Y1 - 2005/11/1

N2 - The rank of a q-ary code C is the dimension of the subspace spanned by C. The kernel of a q-ary code C of length n can be defined as the set of all translations leaving C invariant. Some relations between the rank and the dimension of the kernel of q-ary 1-perfect codes, over script F signq = GF(q) as well as over the prime field script F signp, are established. Q-ary 1-perfect codes of length n=(q m - 1)/(q - 1) with different kernel dimensions using switching constructions are constructed and some upper and lower bounds for the dimension of the kernel, once the rank is given, are established. © 2005 Springer Science+Business Media, Inc.

AB - The rank of a q-ary code C is the dimension of the subspace spanned by C. The kernel of a q-ary code C of length n can be defined as the set of all translations leaving C invariant. Some relations between the rank and the dimension of the kernel of q-ary 1-perfect codes, over script F signq = GF(q) as well as over the prime field script F signp, are established. Q-ary 1-perfect codes of length n=(q m - 1)/(q - 1) with different kernel dimensions using switching constructions are constructed and some upper and lower bounds for the dimension of the kernel, once the rank is given, are established. © 2005 Springer Science+Business Media, Inc.

KW - Kernel

KW - Nonlinear codes

KW - Perfect codes

KW - Rank

KW - q-ary codes

U2 - https://doi.org/10.1007/s10623-004-3989-x

DO - https://doi.org/10.1007/s10623-004-3989-x

M3 - Article

VL - 37

SP - 243

EP - 261

ER -

Kernels and p-kernels of pr -ary 1-perfect codes

Abstract

Keywords

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