3 problems

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Generalized conjecture on the asymptotic improvement of the $q$ -ary Gilbert–Varshamov bound
Let $A_q(n,d)$ denote the maximum size of a $q$ -ary code of length $n$ and minimum distance $d$ , and let … The bound obtained from the $q$ -ary construction should satisfy the $q$ -a…
Conjectureopencoding-theory gilbert-varshamov-bound q-ary-codesarXiv posted 2 days ago
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Balanced triples attaining finite-degree GV
Let $(j_Z,j_X,k)$ be any balanced triple satisfying … The corresponding HA-side and MN-side classical constituent codes are the codes associated with this triple, and a balanced tr…
Conjectureopengilbert-varshamov-bound quantum-error-correction quantum-ldpc-codesarXiv posted 2 days ago
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The binary Gilbert–Varshamov bound conjecture
Let $A_2(n,d)$ denote the maximum number of codewords in a binary code of length $n$ and minimum Hamming distance $d$ . For relative distance $delta$ and rate $R$ , consider families…
Conjectureopencoding-theory gilbert-varshamov-boundarXiv posted 2 days ago

Generalized conjecture on the asymptotic improvement of the qqq-ary Gilbert–Varshamov bound