Griesmer codes, Grey–Rankin bound and the projective dual transform
DOI:
https://doi.org/10.55630/mem.2026.55.370-381Keywords:
Griesmer bound, Grey–Rankin bound, projective dual transformAbstract
Professor Stefan Dodunekov made influential contributions across several domains of coding theory, number theory, and algebra. In this survey we focus on three areas in which his scientific interests were particularly substantial. The first two concern families of linear codes meeting the Griesmer bound and the Grey–Rankin bound, which have long served as central benchmarks in the study of optimal codes. The third theme is the projective dual transform, which has proven essential in the study of codes related to these bounds, and which has offered a unifying geometric and algebraic framework. Based on his contributions to this field, we emphasize both their prominence and their continuing influence on contemporary research related to various classes and families of linear codes over a finite field.
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