Every projective linear code can be converted, via a simplex complementary code and a length extension, into a minimal linear code violating the Ashikhmin-Barg condition.
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Minimal Linear Codes Violating the Ashikhmin-Barg Condition from Arbitrary Projective Linear Codes
Every projective linear code can be converted, via a simplex complementary code and a length extension, into a minimal linear code violating the Ashikhmin-Barg condition.