On Symbol-Pair Distance of a Class of Constacyclic Codes of Length 3<i>p^s</i> over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></mrow></semantics></math></inline-formula>

Abstract

Let p≠3 be any prime. In this paper, we compute symbol-pair distance of all γ-constacyclic codes of length 3ps over the finite commutative chain ring R=Fpm+uFpm, where γ is a unit of R which is not a cube in Fpm. We give the necessary and sufficient condition for a symbol-pair γ-constacyclic code to be an MDS symbol-pair code. Using that, we provide all MDS symbol-pair γ-constacyclic codes of length 3ps over R. Some examples of the symbol-pair distance of γ-constacyclic codes of length 3ps over R are provided.

Keywords

• constacyclic codes
• dual codes
• chain rings
• MDS codes
• symbol-pair codes