International audienceLinear codes over finite rings are described here as trace codes for a suitable generalization of the trace called a GF-trace. Cyclic codes over Galois rings are given a trace description as well. The main tools are the notion of trace dual bases, in the case of linear codes, and of normal bases of an extension ring over a ring, in the case of cyclic codes
i, u1u2 − u2u1,..., ukuj − ujuk,...), and Fq[u, v]/ ui, vj, uv − vu, where Fq is a field with q ele-...
Abstract. The uniform distribution of the trace map lends itself very well to the construction of bi...
Cyclic codes give us the most probable method by which we may detect and correct data transmission e...
We present linear codes over finite commutative rings which are not necessarily Frobenius. We treat ...
We introduce linear cyclic codes over the ring F 2 + uF 2 = f0; 1; u; u = u + 1g, where u 2 = 0. T...
ISBN 978-84-608-6082-2We introduce a new type of linear and cyclic codes. These codes are defined ov...
This work is focused on linear error-correcting codes over chain rings. By a linear code over a chai...
. Various forms of the extension problem are discussed for linear codes defined over finite rings. T...
Codes over finite rings have been studied in the early 1970’s [4]. A great deal of attention has bee...
This paper discusses the foundations of the theory of linear codes defined over finite modules. Two ...
The construction of two or few-weight codes from trace codes over the ring Fq + uFq, where u2 = 0, w...
The techniques of algebraic geometry have been widely and successfully applied to the study of linea...
It is very well known that algebraic structures have valuable applications in the theory of error-co...
The techniques of algebraic geometry have been widely and successfully applied to the study of linea...
In this work, we define $G$-codes over the infinite ring $R_\infty$ as ideals in the group ring $R_\...
i, u1u2 − u2u1,..., ukuj − ujuk,...), and Fq[u, v]/ ui, vj, uv − vu, where Fq is a field with q ele-...
Abstract. The uniform distribution of the trace map lends itself very well to the construction of bi...
Cyclic codes give us the most probable method by which we may detect and correct data transmission e...
We present linear codes over finite commutative rings which are not necessarily Frobenius. We treat ...
We introduce linear cyclic codes over the ring F 2 + uF 2 = f0; 1; u; u = u + 1g, where u 2 = 0. T...
ISBN 978-84-608-6082-2We introduce a new type of linear and cyclic codes. These codes are defined ov...
This work is focused on linear error-correcting codes over chain rings. By a linear code over a chai...
. Various forms of the extension problem are discussed for linear codes defined over finite rings. T...
Codes over finite rings have been studied in the early 1970’s [4]. A great deal of attention has bee...
This paper discusses the foundations of the theory of linear codes defined over finite modules. Two ...
The construction of two or few-weight codes from trace codes over the ring Fq + uFq, where u2 = 0, w...
The techniques of algebraic geometry have been widely and successfully applied to the study of linea...
It is very well known that algebraic structures have valuable applications in the theory of error-co...
The techniques of algebraic geometry have been widely and successfully applied to the study of linea...
In this work, we define $G$-codes over the infinite ring $R_\infty$ as ideals in the group ring $R_\...
i, u1u2 − u2u1,..., ukuj − ujuk,...), and Fq[u, v]/ ui, vj, uv − vu, where Fq is a field with q ele-...
Abstract. The uniform distribution of the trace map lends itself very well to the construction of bi...
Cyclic codes give us the most probable method by which we may detect and correct data transmission e...
DOI
Add to ORKG