2020/02/25 by Nupur Patanker, Sanjay Kumar Singh, Patanker, Nupur +1
Computer Science · Engineering · Mathematics · Social Sciences · #06A07) #11T71 #13P25 ( 14G50 #94B27 #Coding theory and cryptography #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Islamic Finance and Communication #cs.IT #graph theory and CDMA systems #math.AC #math.IT #msc:11T71 #msc:13P25 #msc:14G50 #msc:94B27
paper · pdf · doi:10.48550/arxiv.2002.10920
Due to an error in the proof, Lemma 4.6 to Lemma 4.9 has been deleted
openalex publication_date 2020/02/25 · arxiv created 2020/10/25 · arxiv updated 2020/10/27 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Let \mathbbFq be a finite field with q elements, where q is a power of prime p. A polynomial over \mathbbFq is square-free if all its monomials are square-free. In this note, we determine an upper bound on the number of zeroes in the affine torus T=(\mathbbFq*)s of any set of r linearly independent square-free polynomials over \mathbbFq in s variables, under certain conditions on r, s and degree of these polynomials. Applying the results, we partly obtain the generalized Hamming weights of toric codes over hypersimplices and square-free evaluation codes, as defined in \citehyper. Finally, we obtain the dual of these toric codes with respect to the Euclidean scalar product.