A new approach to the Kasami codes of type 2
Abstract
The dual of the Kasami code of length $q^21$, 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 $q1$. 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1810.00015
 Bibcode:
 2018arXiv181000015S
 Keywords:

 Computer Science  Information Theory;
 Mathematics  Combinatorics;
 05E30;
 94B05
 EPrint:
 Revised version. The automorphismgroup part essentially updated (in the previous versions, it contained incorrect results)