A new approach to the Kasami codes of type 2

09/28/2018

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by   Minjia Shi, et al.

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The dual of the Kasami code of length q^2-1, with q a power of 2, is constructed by concatenating a cyclic MDS code of length q+1 over F_q, with a simplex code of length q-1. This yields a new derivation of the weight distribution of the Kasami code, a new description of its coset graph, and a new proof that the Kasami code is completely regular. The concatenation construction allows us to determine completely the automorphism group of the Kasami code. New cyclic completely regular codes over finite fields a power of 2 are constructed. They have coset graphs isomorphic to that of the Kasami codes.