2 problems

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Shi–Zhu–Helleseth's Griesmer bound conjecture for cyclic codes in the $b$ -symbol metric
Let $q$ be a prime power, let $b$ be a positive integer, and let $t$ be a positive integer. Let $k=t b$ , and let ${\mathcal C}$ be an $(n,k,d_b)^b_q$ cyclic code, where $d_b$ denot…
Conjectureopengriesmer-bound linear-codes symbol-metricarXiv posted 2 days ago
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Systematic codes violating the Griesmer bound at distance $2^r+2$
Systematic-code Griesmer conjecture. For every integer $r\geq 3$ , there exists a systematic code with distance $2^r+2$ that does not satisfy the Griesmer bound.
Conjectureopencoding-theory griesmer-bound systematic-codesarXiv posted 2 days ago

Shi–Zhu–Helleseth's Griesmer bound conjecture for cyclic codes in the bbb-symbol metric