A classification of Fpᵏ-braces using bilinear forms

Let Fpᵏ be a finite field of odd characteristic p. In this paper we give a classification, up to isomorphism, of the associative commutative Fpᵏ-algebras such that the resulting ring is radical, starting from the connection with their bi-brace structure. Such classification is the generalization in odd characteristic of the result proved by Civino at al. in characteristic $2$.