Constacyclic Codes of Length 3<italic>p</italic>^{<italic>s</italic>} Over F<italic>_p</italic>^{<italic>m</italic>} &#x002B; <italic>u</italic>F<italic>_p</italic>^{<italic>m</italic>} and Their Application in Various Distance Distributions

• Main Authors: Hai Q. Dinh, Bac Trong Nguyen, Woraphon Yamaka
• Format: Article
• Language: English
• Published: IEEE 2020-01-01
• Series: IEEE Access
• Subjects: Repeated-root codes; hamming distance; RT distance; homogeneous distance
• Online Access: https://ieeexplore.ieee.org/document/9249409/

Let p &#x2260; 3 be any prime. The structures of all &#x03BB;-constacyclic codes of length 3p^s over the finite commutative chain ring Fp^m + uFp^m (u² = 0) are established in the term of their generator polynomials. As an application, Hamming and homogeneous distance of a class of such codes and RT distances of all are given. Among such &#x03BB;-constacyclic codes, the unique maximum-distance-separable (briefly, MDS) code with respect to the RT distance is obtained. Moreover, when &#x03BB; is not a cube in Fpm, the necessary and sufficient condition for the &#x03BB;-constacyclic code of length 3p^s over Fp^m + uFp^m (u² = 0) be an MDS constacyclic code with respect to Hamming distance is provided.