Linear ℓ-Intersection Pairs of Codes and Their Applications
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In this paper, a linear ℓ-intersection pair of codes is introduced as a generalization of linear complementary pairs of codes. Two linear codes are said to be a linear ℓ-intersection pair if their intersection has dimension ℓ. A characterization of such pairs of codes is given in terms of the corresponding generator and parity-check matrices. Linear ℓ-intersection pairs of MDS codes over F_q of length up to q+1 are given for all possible parameters. As an application, linear ℓ-intersection pairs of codes are used to construct entanglement-assisted quantum error correcting codes. This provides a large number of new MDS entanglement-assisted quantum error correcting codes.
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