3 citations · 3 across the 7 of their papers we have counts for
9 papers
Necessary and sufficient conditions on the order of a finite field for the easy identification of primitive polynomials of degree 2
Gerardo Vega
We present the necessary and sufficient conditions on the order of a finite field such that every irreducible polynomial of the form $x^2+bx+c \in \mathbb{F}_q[x…
A characterization and an explicit description of all primitive polynomials of degree two over finite fields
Gerardo Vega
For polynomials of degree two over finite fields, we present an improvement of Fitzgerald's characterization (Finite Fields Appl. 9(1):117-121, 2003). We then use this new characte…
The b-symbol weight distributions of all semiprimitive irreducible cyclic codes
Gerardo Vega
Up to a new invariant , the complete -symbol weight distribution of a particular kind of two-weight irreducible cyclic codes, was recently obtained by Zhu et al. [Des. Cod…
The complete weight enumerator of a subclass of optimal three-weight cyclic codes
Gerardo Vega, Félix Hernández
A class of optimal three-weight cyclic codes of dimension 3 over any finite field was presented by Vega [Finite Fields Appl., 42 (2016) 23-38]. Shortly thereafter, Heng and Yue [IE…
Optimal three-weight cyclic codes whose duals are also optimal
Gerardo Vega, Félix Hernández
A class of optimal three-weight cyclic codes of dimension 3 over any finite field was presented by Vega [Finite Fields Appl., 42 (2016) 23-38]. Shortly thereafter, Heng and Yue [IE…
An extended characterization of a class of optimal three-weight cyclic codes over any finite field
Gerardo Vega
A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Shortly after this, a generalization for the…
Determining the full weight distribution of any irreducible cyclic code over any finite field of dimension two
Gerardo Vega
In coding theory, a very interesting problem (but at the same time, a very difficult one) is to determine the weight distribution of a given code. This problem is even more interes…
A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field
Gerardo Vega
It is well known that the problem of determining the weight distributions of families of cyclic codes is, in general, notoriously difficult. An even harder problem is to find chara…
Reducible Cyclic Codes Constructed as the Direct Sum of Two Semiprimitive Cyclic Codes
Gerardo Vega
We present a family of reducible cyclic codes constructed as the direct sum of two different semiprimitive two-weight irreducible cyclic codes. This family generalizes the class of…