Linear codes have been widely used in communication systems since the beginning of the digital age. Mathematical research focused on error-correcting codes because of their important applications in data transmission. However, a special type of linear codes, called minimal, has proven to be useful for defining access structures in secret sharing schemes and secure two-party computation. This motivated research in this field.

Minimal codes can be constructed using a simple condition first proposed by Ashikhmin and Barg in 1998. Until the groundbreaking work of Ding, Heng and Zhou in 2018 there were no known examples of infinite families of minimal codes that violated this condition. Since then, several examples of such families have been constructed.

In this talk we present three generic constructions of families of minimal codes that violate Ashikhmin and Barg’s condition based on characteristic functions of suitable sets. This is a joint work with E. Pasalic, F. Zhang and Y. Wei.

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