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Polar codes are constructed based on the reliability of sub-channels resulting from the polarization effect. However, this information-theoretic construction approach leads to a poor weight distribution. To address this issue,…
The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of…
This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction.…
Bent functions can be classified into regular bent functions, weakly regular but not regular bent functions, and non-weakly regular bent functions. Regular and weakly regular bent functions always appear in pairs since their duals are also…
In this paper, we study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a minimal linear code by a character-theoretical…
Recently, Linear Complementary Dual (LCD) codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes. This paper directs its attention to the construction of binary and…
In coding theory, constructing codes with good parameters is one of the most important and fundamental problems. Though a great many of good codes have been produced, most of them are defined over alphabets of sizes equal to prime powers.…
For every linear binary code $C$, we construct a geometric triangular configuration $\Delta$ so that the weight enumerator of $C$ is obtained by a simple formula from the weight enumerator of the cycle space of $\Delta$. The triangular…
Linear codes with large minimal distances are important error correcting codes in information theory.Orthogonal codes have more applications in the other fields of mathematics. In this paper, we study the binary and ternary orthogonal codes…
We confirm a conjecture of Cun Sheng Ding~\cite{Ding-Discrete} claiming that the punctured value-sets of a list of eleven trinomials over odd-degree extensions of the binary field give rise to difference sets with Singer parameters. In the…
In this paper, we construct a large family of projective linear codes over ${\mathbb F}_{q}$ from the general simplicial complexes of ${\mathbb F}_{q}^m$ via the defining-set construction, which generalizes the results of [IEEE Trans. Inf.…
Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not…
In this paper, we discuss the generalized Hamming weights of a class of linear codes associated with non-degenerate quadratic forms. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting…
The rapid development of large pre-trained language models has greatly increased the demand for model compression techniques, among which quantization is a popular solution. In this paper, we propose BinaryBERT, which pushes BERT…
The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their constructions. In this paper, we study the problem…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…
It is known that a linear two-weight code $C$ over a finite field $\F_q$ corresponds both to a multiset in a projective space over $\F_q$ that meets every hyperplane in either $a$ or $b$ points for some integers $a<b$, and to a strongly…
We study the generalized and extended weight enumerator of the q-ary Simplex code and the q-ary first order Reed-Muller code. For our calculations we use that these codes correspond to a projective system containing all the points in a…
In this paper, based on the theory of defining sets, a class of four-weight or five-weight linear codes over Fp is constructed. The complete weight enumerators of the linear codes are determined by means of Weil sums. In some case, there is…
We consider (symmetric, non-degenerate) bilinear spaces over a finite field and investigate the properties of their $\ell$-complementary subspaces, i.e., the subspaces that intersect their dual in dimension $\ell$. This concept generalizes…