A Sequence of Unique Quaternary Griesmer Codes |
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| Authors: | Harold N. Ward |
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| Affiliation: | (1) Department of Mathematics, University of Virginia, Charlottesville, VA, 22904, U.S.A. |
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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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| Keywords: | Griesmer bound quaternary code Hermitian form divisible code residual code MacWilliams identities |
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