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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

Systematic codes violating the Griesmer bound at distance 2r+22^r+22r+2