On components of a Kerdock code and the dual of the BCH code C_1,3

10/10/2018

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by   I. Yu. Mogilnykh, et al.

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In the paper we investigate the structure of i-components of two classes of codes: Kerdock codes and the duals of the primitive cyclic BCH code with designed distance 5 of length n=2^m-1, for odd m. We prove that for any admissible length a punctured Kerdock code consists of two i-components and the dual of BCH code is a i-component for any i. We give an alternative proof for the fact presented by De Caen and van Dam in 1999 that the restriction of the Hamming scheme to a doubly shortened Kerdock code is an association scheme.