相关论文: Convolutional Goppa Codes

Classes of self-dual codes and dual-containing codes are constructed. The codes are obtained within group rings and, using an isomorphism between group rings and matrices, equivalent codes are obtained in matrix form. Distances and other…

For a given curve X and divisor class C, we give lower bounds on the degree of a divisor A such that A and A-C belong to specified semigroups of divisors. For suitable choices of the semigroups we obtain (1) lower bounds for the size of a…

A method of constructing algebraic-geometric codes with many automorphisms arising from Galois points for algebraic curves is presented.

Let $\X$ be an algebraic curve of genus $g \geq 2$ defined over a field $\F_q$ of characteristic $p > 0$. From $\X$, under certain conditions, we can construct an algebraic geometry code $C$. If the code $C$ is self-orthogonal under the…

Classical Goppa codes are a well-known class of codes with applications in code-based cryptography, which are a special case of alternant codes. Many papers are devoted to the search for Goppa codes with a cyclic extension or with a cyclic…

In recent years, linear complementary pairs (LCP) of codes and linear complementary dual (LCD) codes have gained significant attention due to their applications in coding theory and cryptography. In this work, we construct explicit LCPs of…

We construct pairs of elliptic curves over number fields with large intersection of projective torsion points.

We study $q$-ary codes with distance defined by a partial order of the coordinates of the codewords. Maximum Distance Separable (MDS) codes in the poset metric have been studied in a number of earlier works. We consider codes that are close…

We provide a new construction of $[n,9,n-9]_q$ near-MDS codes arising from elliptic curves with $n$ ${\mathbb F}_q$-rational points. Furthermore we show that in some cases these codes cannot be extended to longer near-MDS codes.

Linear complementary dual (LCD) codes and linear complementary pairs (LCP) of codes have been proposed for new applications as countermeasures against side-channel attacks (SCA) and fault injection attacks (FIA) in the context of direct sum…

In the realm of algebraic geometric (AG) codes, characterizing dual codes has long been a challenging task. In this paper we introduces a generalized criterion to characterize self-orthogonality of AG codes based on residues, drawing upon…

In this note, we give a construction of codes on algebraic function field $F/ \mathbb{F}_{q}$ using places of $F$ (not necessarily of degree one) and trace functions from various extensions of $\mathbb{F}_{q}$. This is a generalization of…

In this paper, we introduce multivariate Goppa codes, which contain as a special case the well-known, classical Goppa codes. We provide a parity check matrix for a multivariate Goppa code in terms of a tensor product of generalized…

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…

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary…

The determination of the maximal length of maximum distance separable (MDS) codes arising from elliptic curves is a central problem in coding theory. For an elliptic curve $E$ over $\mathbb{F}_q$, let $\operatorname{MEC}(k,q)$ denote the…

In this paper, we present a construction of locally recoverable codes (LRCs) with multiple recovery sets using algebraic curves with many rational points. By leveraging separable morphisms between smooth projective curves and expanding the…

Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based…

We introduce a new construction of error-correcting codes from algebraic curves over finite fields. Modular curves of genus g -> infty over a field of size q0^2 yield nonlinear codes more efficient than the linear Goppa codes obtained from…

Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. We introduce two new families of quantum convolutional codes. Our construction is based on an algebraic method which allows to…