On the number of slopes of the graph of a function defined on a finite field
Journal of Combinatorial Theory Series A
Introduction to Coding Theory
Linear Point Sets and Rédei Type k-blocking Sets in PG(n, q)
Journal of Algebraic Combinatorics: An International Journal
The number of directions determined by a function over a finite field
Journal of Combinatorial Theory Series A
Small Complete Arcs in Projective Planes
Combinatorica
Cryptography, Information Theory, and Error-Correction: A Handbook for the 21st Century
Cryptography, Information Theory, and Error-Correction: A Handbook for the 21st Century
Introduction to Coding Theory
Maximum distance separable codes and arcs in projective spaces
Journal of Combinatorial Theory Series A
On the graph of a function in many variables over a finite field
Designs, Codes and Cryptography
Coprimitive sets and inextendable codes
Designs, Codes and Cryptography
Applicable Algebra in Engineering, Communication and Computing
Bounds on (n,r)-arcs and their application to linear codes
Finite Fields and Their Applications
Small Complete Arcs in PG(2,p)
Finite Fields and Their Applications
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We show that if a linear code admits an extension, then it necessarily admits a linear extension. There are many linear codes that are known to admit no linear extensions. Our result implies that these codes are in fact maximal. We are able to characterize maximal linear (n, k, d) q -codes as complete (weighted) (n, n 驴 d)-arcs in PG(k 驴 1, q). At the same time our results sharply limit the possibilities for constructing long non-linear codes. The central ideas to our approach are the Bruen-Silverman model of linear codes, and some well known results on the theory of directions determined by affine point-sets in PG(k, q).