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

04/02/2022

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by   Sanjit Bhowmick, et al.

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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.