On the affine permutation group of certain decreasing Cartesian codes
Eduardo Camps Moreno, Hiram López, Virginia Tech, United States; Eliseo Sarmiento, Instituto Politécnico Nacional, Mexico; Ivan Soprunov, Cleveland State University, United States
Session:
Combinatorial Coding Theory 3
Track:
1: Algebraic Aspects of Coding Theory
Location:
Ypsilon IV-V-VI
Presentation Time:
Fri, 12 Jul, 12:10 - 12:30
Session Chair:
Hiram Lopez,
Abstract
A decreasing Cartesian code is defined by evaluating a monomial set closed under divisibility on a Cartesian set. Some well-known examples are the Reed-Solomon, Reed-Muller, and (some) toric codes. The affine permutations consist of the permutations of the code that depend on an affine transformation. In this work, we study the affine permutations of some decreasing Cartesian codes, including the case when the Cartesian set has copies of multiplicative or additive subgroups.