BCH codes with larger dimensional hull

摘要

Hulls of linear codes are widely studied due to their good properties and wide applications. Let n = q(m-1)/r and C be an [n, k] cyclic code over F-q, where r vertical bar q- 1. In this paper, we present several necessary and sufficient conditions for BCH codes of length n that have k - 1 or k(perpendicular to) - 1 dimensional hulls, where k. is the dimension of C-perpendicular to. Further, we give the parameters of several families of self-orthogonal codes that arise as hulls of BCH codes. We obtainmany optimal codes.

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