Linear intersection pairs of abelian codes over finite fields and applications

Recently, linear intersection pairs of linear codes have been introduced as a generalization of complementary dual codes, linear complementary pairs, and hulls of linear codes. Such pairs have been of interest due to their nice algebraic properties and wide applications. This paper focuses on linear intersection pairs of abelian codes in semisimple and principal ideal group algebras Formula: see text, where Formula: see text is a finite field and Formula: see text is a finite abelian group. Necessary and sufficient conditions for the existence of a linear intersection pair of abelian codes in Formula: see text with prescribed intersecting dimension are presented. Constructions of linear intersection pairs of abelian codes in Formula: see text of a fixed intersecting dimension are given. Subsequently, the characterization and construction of linear complementary pairs of abelian codes in Formula: see text are established. As applications, constructions of entanglement-assisted quantum error-correcting codes are briefly outlined using these pairs.