I am trying to show that a code with length 13, dimension 6 and minimal distance 5 over $\mathbb{F}_q$ does not exist. I am confused though, doesn't this depend on $q$? I am also asked to show that such a code would satisfy the Hamming bound and Singleton bound but the Hamming bound also depends on $q$ right? Is there a way to show this directly?
2026-04-03 04:17:21.1775189841
Existence of a linear [13,6,5] code
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