Related papers: On the weight distribution of random binary linear…
For $0 < \lambda < 1$ and $n \rightarrow \infty$ pick uniformly at random $\lambda n$ vectors in $\{0,1\}^n$ and let $C$ be the orthogonal complement of their span. Given $0 < \gamma < \frac12$ with $0 < \lambda < h(\gamma)$, let $X$ be the…
A statistical estimation algorithm of the weight distribution of a linear code is shown, based on using its generator matrix as a compression function on random bit strings.
Asymptotic concentration behaviors of linear combinations of weight distributions on the random linear code ensemble are presented. Many important properties of a binary linear code can be expressed as the form of a linear combination of…
Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of…
We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight, i.e., the number of nonzero digit vectors. This leads to efficient linear combination algorithms in abelian…
We estimate the variance of weight and stopping set distribution of regular LDPC ensembles. Using this estimate and the second moment method we obtain bounds on the probability that a randomly chosen code from regular LDPC ensemble has its…
A fundamental property of codes, the second-order weight distribution, is proposed to solve the problems such as computing second moments of weight distributions of linear code ensembles. A series of results, parallel to those for weight…
We study a process of generating random positive integer weight sequences $\{ W_n \}$ where the gaps between the weights $\{ X_n = W_n - W_{n-1} \}$ are i.i.d. positive integer-valued random variables. We show that as long as the gap…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…
Consider a random word $X^n=(X_1,\ldots ,X_n)$ in an alphabet consisting of $4$ letters, with the letters viewed either as $A$, $U$, $G$ and $C$ (i.e., nucleotides in an RNA sequence) or $\alpha$, $\bar{\alpha}$, $\beta$ and $\bar{\beta}$…
The present work analyzes the redundancy of sets of combinatorial objects produced by a weighted random generation algorithm proposed by Denise et al. This scheme associates weights to the terminals symbols of a weighted context-free…
We study the joint distribution of the input sum and the output sum of a deterministic transducer. Here, the input of this finite-state machine is a uniformly distributed random sequence. We give a simple combinatorial characterization of…
We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number $n$ of elements, or a…
Let n be an even positive integer and F be the field \GF(2). A word in F^n is called balanced if its Hamming weight is n/2. A subset C \subseteq F^n$ is called a balancing set if for every word y \in F^n there is a word x \in C such that y…
We consider a uniform distribution on the set $\mathcal{M}_k$ of moments of order $k \in \mathbb{N}$ corresponding to probability measures on the interval $[0,1]$. To each (random) vector of moments in $\mathcal{M}_{2n-1}$ we consider the…
The determination of weight distribution of cyclic codes involves evaluation of Gauss sums and exponential sums. Despite of some cases where a neat expression is available, the computation is generally rather complicated. In this note, we…
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…
Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two…
The analysis of strings of $n$ random variables with geometric distribution has recently attracted renewed interest: Archibald et al. consider the number of distinct adjacent pairs in geometrically distributed words. They obtain the…