On the next-to-minimal weight of affine cartesian codes

详细信息    查看全文

• 作者：Cí ; cero Carvalho ; ¹ ; ^{cicero@ufu.br} ; Victor G.L. Neumann¹ ; ^{victor.neumann@ufu.br}
• 关键词：1T71 ; 14G50 ; 94B60 ; 13P10
• 刊名：Finite Fields and Their Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：44
• 期：Complete
• 页码：113-134
• 全文大小：440 K
• 卷排序：44

文摘

In this paper we determine many values of the second least weight of codewords, also known as the next-to-minimal Hamming weight, for a type of affine variety codes, obtained by evaluating polynomials of degree up to d on the points of a cartesian product of n   subsets of a finite field FqFq. Such codes firstly appeared in a work by O. Geil and C. Thomsen (see [12]) as a special case of the so-called weighted Reed–Muller codes, and later appeared independently in a work by H. López, C. Rentería-Marquez and R. Villarreal (see [16]) named as affine cartesian codes. Our work extends, to affine cartesian codes, the results obtained by Rolland in [17] for generalized Reed–Muller codes.