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A Sequence of Unique Quaternary Griesmer Codes

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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.

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  1. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904, U.S.A.

    Harold N. Ward

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  1. Harold N. Ward
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Ward, H.N. A Sequence of Unique Quaternary Griesmer Codes. Designs, Codes and Cryptography 33, 71–85 (2004). https://doi.org/10.1023/B:DESI.0000032608.92853.95

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  • DOI: https://doi.org/10.1023/B:DESI.0000032608.92853.95

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