Hermitian Self-Dual Cyclic Codes of Length $p^a$ over $GR(p^2,s)$

Abstract

In this paper, we study cyclic codes over the Galois ring $\mathrm{GR}(p^2,s)$. The main result is the characterization and enumeration of Hermitian self-dual cyclic codes of length $p^a$ over $\mathrm{GR}(p^2,s)$. Combining with some known results and the standard Discrete Fourier Transform decomposition, we arrive at the characterization and enumeration of Euclidean self-dual cyclic codes of any length over $\mathrm{GR}(p^2,s)$. Some corrections to results on Euclidean self-dual cyclic codes of even length over ${\mathbb{Z}}_4$ in Discrete Appl. Math. 128, (2003), 27 and Des. Codes Cryptogr. 39, (2006), 127 are provided.

arXiv comment18 pages. Submitted to Advances in Mathematics of Communications