We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-
Muller codes and projective Reed-Muller codes in fewer variables. From this construction …

We give an alternative proof of the formula for the minimum distance of a projective Reed-
Muller code of an arbitrary order. It leads to a complete characterization of the minimum …

By solving a problem regarding polynomials in a quotient ring, we obtain the relative hull
and the Hermitian hull of projective Reed–Muller codes over the projective plane. The …

We give an expository account of Nullstellensatz-like results when the base field is finite. In
particular, we discuss the vanishing ideal of the affine space and of the projective space …

We define a linear code C η (δ T, δ X) by evaluating polynomials of bidegree (δ T, δ X) in the
Cox ring on F q-rational points of a minimal Hirzebruch surface over the finite field F q. We …

Motivated by applications to the theory of error-correcting codes, we give an algorithmic
method for computing a generating set for the ideal generated by $\beta $-graded …

Any integral convex polytope P in ℝ N provides an N-dimensional toric variety XP and an
ample divisor DP on this variety. This paper gives an explicit construction of the algebraic …

We give a recursive decoding algorithm for projective Reed-Muller codes making use of a
decoder for affine Reed-Muller codes. We determine the number of errors that can be …

Rank-metric codes have been a central topic in coding theory due to their theoretical and
practical significance, with applications in network coding, distributed storage, crisscross …

We give a complete conjectural formula for the number er (d, m) of maximum possible F q-
rational points on a projective algebraic variety defined by r linearly independent …