The book is devoted to the theory of algebraic geometric codes, a subject formed on the
border of several domains of mathematics. on one side there are such classical areas as …

The notion of higher (or generalized) weights of codes is just as natural as that of the
classical Hamming weight. The authors adopt the geometric point of view and always treat …

The concept of an error-correcting array gives a new bound on the minimum distance of
linear codes and a decoding algorithm which decodes up to half this bound. This gives a …

The order bound on generalized Hamming weights is introduced in a general setting of
codes on varieties which comprises both the one point geometric Goppa codes as well as …

The rth generalized Hamming weight of a linear code is the minimum support size of any r-
dimensional subcode. It has been found useful in the studies of cryptography and trellis …

On Goppa Codes and Weierstrass Gaps at Several Points⋆ Page 1 Designs, Codes and
Cryptography, 35, 211–225, 2005 © 2005 Springer Science+Business Media, Inc …

This paper presents a formula for $ a $-number of certain maximal curves characterized by
the equation $ y^{\frac {q+ 1}{2}}= x^ m+ x $ over the finite field $\mathbb {F} _ {q^ 2} $. $ a …

This is a self-contained introduction to algebraic curves over finite fields and geometric
Goppa codes. There are four main divisions in the book. The first is a brief exposition of …

The generalized Hamming weights dr (C) of a linear code C are a natural generalization of
the minimum Hamming distance d (C)[= d 1 (C)] and have become an important research …

The minimum support weight, d/sub r/(C), of a linear code C over GF (q) is the minimal size
of the support of an r-dimensional subcode of C. A number of bounds on d/sub r/(C) are …