相关论文: The extended coset leader weight enumerator of a t…

Product codes are widely used in data-storage, optical and wireless applications. Their analytical performance evaluation usually relies on the truncated union bound, which provides a low error rate approximation based on the minimum…

The paper describes a method to determine symmetrized weight enumerators of $p^m$-linear codes based on the notion of a disjoint weight enumerator. Symmetrized weight enumerators are given for the lifted quadratic residue codes of length 24…

In this paper we give a complete characterization of the intersections between the Norm-Trace curve over $\mathbb{F}_{q^3}$ and the curves of the form $y=ax^3+bx^2+cx+d$, generalizing a previous result by Bonini and Sala, providing more…

We study the interaction between the group law on an elliptic curve and the additive structure of $x$-coordinates of rational points on an elliptic curve. Let $E/\mathbb{Q}$ be an elliptic curve of Mordell-Weil rank $r \geq 1$, $d \geq 1$…

For any q which is a power of 2 we describe a finite subgroup of the group of invertible complex q by q matrices under which the complete weight enumerators of generalized doubly-even self-dual codes over the field with q elements are…

In this article, we show explicitly all possible weight enumerators for every irreducible cyclic code of length $n$ over a finite field $\mathbb F_q$, in the case which each prime divisor of $n$ is also a divisor of $q-1$.

Linear codes with a few weights have wide applications in information security, data storage systems, consuming electronics and communication systems. Construction of the linear codes with a few weights and determination of their parameters…

We consider the weight distributions of the cosets of weight 2 of the generalized $[q+1,q+2-d,d]_q$ doubly extended Reed-Solomon codes (GDRS) of minimum distance $d\ge5$, over the finite field $\mathbb{F}_q$ with $q$ elements. For a GDRS…

In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, this need not be the case for twisted RS codes. Nonetheless,…

A codeword is associated to a linearized polynomial. The weight distribution of the codewords is determined as the linearized polynomial varies in a family of fixed degree. There is a corresponding result on Wenger graphs from linearized…

Determining the weight distribution of a code is an old and fundamental topic in coding theory that has been thoroughly studied. In 1977, Helleseth, Kl{\o}ve, and Mykkeltveit presented a weight enumerator polynomial of the lifted code over…

The paper has a threefold purpose. The first purpose is to present an explicit description of expanded cyclic codes defined in $\GF(q^m)$. The proposed explicit construction of expanded generator matrix and expanded parity check matrix…

Linear codes with a few weights are an important class of codes in coding theory and have attracted a lot of attention. In this paper, we present several constructions of $q$-ary linear codes with two or three weights from vectorial…

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime power $q$, we construct some class of linear code over finite field $\mathbb{F}_q$ with defining set be the preimage of…

A subset $\mathcal{S}$ of a conic $\mathcal{C}$ in the projective plane $\mathrm{PG}(2,q)$ is called almost complete (AC-subset for short) if it can be extended to a larger arc in $\mathrm{PG}(2,q)$ only by the points of…

The deep holes of a linear code are the vectors that achieve the maximum error distance (covering radius) to the code. {Determining the covering radius and deep holes of linear codes is a fundamental problem in coding theory. In this paper,…

We study the problem of the existence of arithmetic progressions of three cubes over quadratic number fields Q(sqrt(D)), where D is a squarefree integer. For this purpose, we give a characterization in terms of Q(sqrt(D))-rational points on…

Let $\mathbb{F}_q$ be a finite field of size $q$ and $\mathbb{F}_q^*$ the set of non-zero elements of $\mathbb{F}_q$. In this paper, we study a class of twisted generalized Reed-Solomon code $C_\ell(D, k, \eta, \vec{v})\subset…

One-weight codes, in which all nonzero codewords share the same weight, form a highly structured class of linear codes with deep connections to finite geometry. While their classification is well understood in the Hamming and rank metrics -…

Motivated by applications in distributed storage, distributed computing, and homomorphic secret sharing, we study communication-efficient schemes for computing linear combinations of coded symbols. Specifically, we design low-bandwidth…