Skew cyclic codes over Fq [u1, u2, …, ur ]/⟨u3i− u i, ui uj − uj ui ⟩ri,j=1

Abstract

Our paper delves into exploring skew cyclic codes over a generalized class of rings denoted by T = Tr. We define Tr = Fq [u1, u2, …, ur ]/⟨u3i− ui, ui uj − uj ui ⟩ri,j=1,q=pm and p is some odd prime. Our study introduces a Gray map for the ring T and explores its properties. Using a decomposition theorem, we analyze the structural features of skew cyclic codes over T. Additionally, we offer a formula to find the count of skew cyclic codes of length n over the ring T under specific conditions. Further, we derive a criterion to get Linear Complementary Dual (LCD) codes over T from skew cyclic codes. Moreover, we present a technique for deriving quantum codes from a particular class of skew cyclic codes over T which contain their dual. © Palestine Polytechnic University-PPU 2024.