Research Information System
AIMS Mathematics, vol.9, no.5, pp.11076-11091, 2024 (SCI-Expanded)
In this paper, we introduced double cyclic codes over Rr × Rs, where R = ℤ2 + uℤ2 = {0, 1, u, 1 + u} is the ring with four elements and u2 = 0. We first determined the generator polynomials of R-double cyclic codes for odd integers r and s, then gave the generators of duals of free double cyclic codes over Rr × Rs. By defining a linear Gray map, we looked at the binary images of R-double cyclic codes and gave several examples of optimal parameter binary linear codes obtained from R-double cyclic codes. Moreover, we studied self-dual R-double cyclic codes and presented an example of a self-dual R-double cyclic code.