A Sequence of Unique Quaternary Griesmer Codes

Author: Ward Harold N.  

Publisher: Springer Publishing Company

ISSN: 0925-1022

Source: Designs, Codes and Cryptography, Vol.33, Iss.1, 2004-08, pp. : 71-85

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Abstract

This paper establishes that there is no [98,5,72]_{4} code. Such a code would meet the Griesmer bound and the weights of its codewords would all be divisible by 4. The proof of nonexistence uses the uniqueness of codes with parameters [n,4,n - 5]4,14 ≤ n ≤ 17. The uniqueness of these codes for n ≥ 15 had been established geometrically by others; but it is rederived here, along with that of the [14,4,9]4 code, by exploiting the Hermitian form obtained when the weight function is read modulo 2.