The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

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 …

Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on
algebraic curves over finite fields have been an important research topic for algebraic …

It has been known for a long time that the Deligne–Lusztig curves associated to the
algebraic groups of type^ 2A_2,\,^ 2B_2 and^ 2G_2 defined over the finite field F _n all have …

This book is mainly devoted to some computational and algorithmic problems in finite fields
such as, for example, polynomial factorization, finding irreducible and primitive polynomials …

These tables record results on curves with many points over finite fields. For relatively small
genus ($0\leq g\leq 50$) and $ q $ a small power of $2 $ or $3 $ we give in two tables the …

We prove that elements of the Weierstrassgap set of a pair of points may be used to define a
geometricGoppa code which has minimum distance greater than the usuallower bound. We …

Symbol-pair codes were introduced by Cassuto and Blaum in 2010 to protect pair errors in
symbol-pair read channels. Recently Yaakobi, Bruck and Siegel (2016) generalized this …

We present two new constructions of entanglement-assisted quantum error-correcting codes
using some fundamental properties of (classical) linear codes in an effective way. The main …

For the Hermitian curve H defined over the finite field, we give a complete classification of
Galois coverings of H of prime degree. The corresponding quotient curves turn out to be …