On the linear 𝓁-intersection pair of codes over a finite principal ideal ring

A BSTRACT . Generalizing the linear complementary dual, the linear complementary pair and the hull of codes, we introduce linear ℓ -intersection pair of codes over a finite principal ideal ring R, for some positive integer ℓ . Two linear codes are said to be a linear ℓ -intersection pair of codes over R if the cardinality of the intersection of two linear codes are equal to q ℓ , where q is the cardinality of the radical of R. In this paper, we study linear ℓ -intersection pair of codes over R in a very general setting by a uniform method. We provide a necessary and sufficient condition for a non-free (or free) linear ℓ -intersection pair of codes over R.