Locally Recoverable Codes from Algebraic Curves and Surfaces
Alexander Barg, Kathryn Haymaker, Everett W. Howe, Gretchen L. Matthews, Anthony Várilly‐Alvarado · Association for Women in Mathematics series · 2017
A code $$\mathcal{C}$$ of length n over a finite field F q is a subset of the linear space F q n . The code is called linear if it forms a linear subspace of F q n . The minimum distance d of a code is the minimum pairwise separation between two distinct elements of $$\mathcal{C}$$ in the Hamming metric, and if the code $$\mathcal{C}$$ is linear, then d is equal to the minimum Hamming weight of a nonzero codeword of $$\mathcal{C}$$ . We use the notation (n, k, d) to refer to the parameters of a linear k-dimensional code of length n and minimum distance d.