On the minimum distance and the minimum weight of Goppa codes from a quotient of the Hermitian curve

Abstract

In this paper we study evaluation codes arising from plane quotients of the Hermitian curve, defined by affine equations of the form $y^q+y=x^m$, $q$ being a prime power and $m$ a positive integer which divides $q+1$. The dual minimum distance and minimum weight of such codes are studied from a geometric point of view. In many cases we completely describe the minimum-weight codewords of their dual codes through a geometric characterization of the supports, and provide their number. Finally, we apply our results to describe Goppa codes of classical interest on such curves.

Applicable Algebra in Engineering, Communication and Computing (to appear)

References in corpus (3)

• Computing symmetric rank for symmetric tensors
• The dual minimum distance of arbitrary dimensional algebraic--geometric codes
• Hermitian codes from higher degree places

Cited by in corpus (1)

• On the Hermitian curve and its intersections with some conics