Designs and their codes
The number of directions determined by a function f on a finite field
Journal of Combinatorial Theory Series A
On (q^2 + q + 2, q + 2)-arcs in the Projective Plane {\rm PG}(2, q)
Designs, Codes and Cryptography
Designs, Graphs, Codes, and Their Links
Designs, Graphs, Codes, and Their Links
A geometric approach to classifying Griesmer codes
Designs, Codes and Cryptography
On the code generated by the incidence matrix of points and hyperplanes in PG(n,q) and its dual
Designs, Codes and Cryptography
A bound for error-correcting codes
IBM Journal of Research and Development
A study of (x(q + 1), x; 2, q)-minihypers
Designs, Codes and Cryptography
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We study (xv"t,xv"t"-"1)-minihypers in PG(t,q), i.e. minihypers with the same parameters as a weighted sum of x hyperplanes. We characterize these minihypers as a nonnegative rational sum of hyperplanes and we use this characterization to extend and improve the main results of several papers which have appeared on the special case t=2. We establish a new link with coding theory and we use this link to construct several new infinite classes of (xv"t,xv"t"-"1)-minihypers in PG(t,q) that cannot be written as an integer sum of hyperplanes.