Abstract
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 automorphism groups of the Kasami code and the related $q$-ary MDS code are determined. 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.
Highlights
A New Approach to the Kasami Codes of Type 2Abstract— The dual of the Kasami code of length q2 − 1, with q a power of 2, is constructed by concatenating a cyclic MDS code of length q + 1 over Fq with a Simplex code of length q − 1
D ISTANCE-REGULAR graphs form the most extensively studied class of structured graphs due to their many connections with codes, designs, groups and orthogonal polynomials [1], [6]
This gives a new derivation of its weight distribution, a non trivial calculation in [13], and a characterization of its automorphism group
Summary
Abstract— The dual of the Kasami code of length q2 − 1, with q a power of 2, is constructed by concatenating a cyclic MDS code of length q + 1 over Fq 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. New cyclic completely regular codes over finite fields a power of 2, generalized Kasami codes, are constructed; they have coset graphs isomorphic to that of the Kasami codes.
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