Kernels and <Emphasis Type="Italic">p</Emphasis>-Kernels of <Emphasis Type="Italic">p</Emphasis><Superscript><Emphasis Type="Italic">r</Emphasis></Superscript>-ary 1-Perfect Codes期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Kernels and p-Kernels of pr-ary 1-Perfect Codes

Authors:	K.?T.?Phelps,J.?Rifà,M.?Villanueva mailto:merce.villanueva@uab.es" title=" merce.villanueva@uab.es" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	(1) Discrete and Statistical Sciences, Auburn University, Auburn, Al 36849-5307, USA;(2) Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain;(3) Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

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 $mathbb{F}_{q} = GF(q)$ as well as over the prime field $mathbb{F}_{p}$ , 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.Communicated by: I.F. Blake

Keywords:	q-ary codes perfect codes nonlinear codes rank kernel
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