相关论文: Hermitian codes and complete intersections
In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes additive codes. We study MDS codes in this setting and define…
Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form $q=2am+t$,…
The $p$-ary code associated with the incidence structure of points and $t$-spaces in a projective space $\mathrm{PG}(m,q)$, where $q=p^h$, is the $\mathbb{F}_p$-subspace generated by the incidence vectors of the blocks of this design. The…
This paper presents a new decoding for polynomial residue codes, called the minimum degree-weighted distance decoding. The newly proposed decoding is based on the degree-weighted distance and different from the traditional minimum Hamming…
In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing…
Computing the minimum distance of a linear code is one of the fundamental problems in algorithmic coding theory. Vardy [14] showed that it is an \np-hard problem for general linear codes. In practice, one often uses codes with additional…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
This paper investigates certified upper bounds on the minimum distance of an explicit family of Calderbank-Shor-Steane quantum LDPC codes constructed from affine permutation matrices. All codes considered here have active Tanner graphs of…
We present a general construction of asymmetric quantum codes based on additive codes under the trace Hermitian inner product. Various families of additive codes over $\F_{4}$ are used in the construction of many asymmetric quantum codes…
Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then…
A $q$-ary code of length $n$, size $M$, and minimum distance $d$ is called an $(n,M,d)_q$ code. An $(n,q^{k},n-k+1)_q$ code is called a maximum distance separable (MDS) code. In this work, some MDS codes over small alphabets are classified.…
We study properties of rank metric and codes in rank metric over finite fields. We show that in rank metric perfect codes do not exist. We derive an existence bound that is the equivalent of the Gilbert--Varshamov bound in Hamming metric.…
The geometric properties of quantum states is fully encoded by the quantum geometric tensor. The real and imaginary parts of the quantum geometric tensor are the quantum metric and Berry curvature, which characterize the distance and phase…
Extending recent work on the Euclidean hull, we derive closed-form ratio decompositions for the number of linear codes with prescribed Hermitian and symplectic hull dimension. The Hermitian ratio admits a uniform lower bound of at least…
We introduce a new class of numerical semigroups, which we call the class of {\it acute} semigroups and we prove that they generalize symmetric and pseudo-symmetric numerical semigroups, Arf numerical semigroups and the semigroups generated…
Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…
In this article, the minimum distance of the dual $C^{\bot}$ of a functional code $C$ on an arbitrary dimensional variety $X$ over a finite field $\F_q$ is studied. The approach consists in finding minimal configurations of points on $X$…
We show that any ternary Euclidean (resp.\ quaternary Hermitian) linear complementary dual $[n,k]$ code contains a Euclidean (resp.\ Hermitian) linear complementary dual $[n,k-1]$ subcode for $2 \le k \le n$. As a consequence, we derive a…
The order bound for the minimum distance of algebraic geometry codes was originally defined for the duals of one-point codes and later generalized for arbitrary algebraic geometry codes. Another bound of order type for the minimum distance…
Let $V$ be a vector space over the finite field $\mathbb{F}_q$ with $q$ elements and $\Lambda$ be the image of the Segre geometry $\mathrm{PG}(V)\otimes\mathrm{PG}(V^*)$ in $\mathrm{PG}(V\otimes V^*)$. Consider the subvariety $\Lambda_{1}$…