Related papers: Classification of binary systematic codes of small…
From a geometric perspective most nonlinear binary classification algorithms, including state of the art versions of Support Vector Machine (SVM) and Radial Basis Function Network (RBFN) classifiers, and are based on the idea of…
A closed form formula of the partition weight enumerator of maximum distance separable (MDS) codes is derived for an arbitrary number of partitions. Using this result, some properties of MDS codes are discussed. The results are extended for…
Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many…
The main result here is a characterisation of binary $2$-neighbour-transitive codes with minimum distance at least $5$ via their minimal subcodes, which are found to be generated by certain designs. The motivation for studying this class of…
Motivated by applications in polymer-based data storage we introduced the new problem of characterizing the code rate and designing constant-weight binary $B_2$-sequences. Binary $B_2$-sequences are collections of binary strings of length…
In this work, we study the computational complexity of the Minimum Distance Code Detection problem. In this problem, we are given a set of noisy codeword observations and we wish to find a code in a set of linear codes $\mathcal{C}$ of a…
We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and…
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…
Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association…
The weight spectra of MDS codes of length $ n $ and dimension $ k $ over the arbitrary alphabets are studied. For all $ q $-ary MDS codes of dimension $ k $ containing the zero codeword, it is shown that all $ k $ weights from $ n $ to $…
This paper proposes a generic formulation that significantly expedites the training and deployment of image classification models, particularly under the scenarios of many image categories and high feature dimensions. As a defining…
Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary…
In the present paper, we give Assmus--Mattson type theorems for codes and lattices. We show that a binary doubly even self-dual code of length 24m with minimum weight 4m provides a combinatorial 1-design and an even unimodular lattice of…
An $[n,k,d]$ linear code is said to be maximum distance separable (MDS) or almost maximum distance separable (AMDS) if $d=n-k+1$ or $d=n-k$, respectively. If a code and its dual code are both AMDS, then the code is said to be near maximum…
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 developed a novel direct algorithm to derive the mass-ratio distribution (MRD) of short-period binaries from an observed sample of single-lined spectroscopic binaries (SB1). The algorithm considers a class of parameterized MRDs and finds…
The linear codes with a few weights have been applied widely in combinatorial designs, secret sharing, association schemes, authentication codes and strongly regular graphs. In this paper, we first correct an erroneous result about the…
Cyclic codes of dimension $2$ over a finite field are shown to have at most two nonzero weights. This extends a construction of Rao et al (2010) and disproves a conjecture of Schmidt-White (2002). We compute their weight distribution, and…
The binary primitive BCH codes are cyclic and are constructed by choosing a subset of the cyclotomic cosets. Which subset is chosen determines the dimension, the minimum distance and the weight distribution of the BCH code. We construct…
We present a novel technique for encoding and decoding constant weight binary codes that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight…