Derive shift-bound lower bounds for genetic-algorithm codes

Determine whether the minimum-distance lower bounds of the record-breaking linear codes discovered by the genetic algorithm can also be obtained using the generalized shift bound for abelian codes.

Background

The paper constructs abelian codes using a generalized shift bound and separately applies a genetic algorithm to search defining sets for abelian codes with strong or record-breaking parameters. For several codes discovered computationally, the reported minimum distances exceed previously known bounds, but the paper does not establish those distances through the shift-bound machinery.

The unresolved issue is whether the shift bound can certify the lower bounds achieved by the record-breaking codes found by heuristic search. Resolving it would connect the computational discoveries with explicit algebraic distance guarantees and could clarify the effectiveness and reach of the shift-bound method for abelian codes beyond the analytically constructed families.