Related papers: Binary sequences with a low correlation via cyclot…
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and…
We consider error-correction coding schemes for adversarial wiretap channels (AWTCs) in which the channel can a) read a fraction of the codeword bits up to a bound $r$ and b) flip a fraction of the bits up to a bound $p$. The channel can…
Professor Cunsheng Ding gave cyclotomic constructions of cyclic codes with length being the product of two primes. In this paper, we study the cyclic codes of length $n=2^e$ and dimension $k=2^{e-1}$. Clearly, Ding's construction is not…
In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ and their binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$ whose defining sets are the certain subsets of $\mathbb{F}_{2^n}^m$ obtained from…
The autocorrelation function and the run structure are two basic notions for binary sequences, and have been used as two independent postulates to test randomness of binary sequences ever since Golomb 1955. In this paper, we prove for…
In this article, we investigate properties of cyclic codes over a finite non-chain ring $\mathbb{F}_q+v\mathbb{F}_q+v^2\mathbb{F}_q+v^3\mathbb{F}_q+v^4\mathbb{F}_q,$ where $q=p^r,$ $r$ is a positive integer, $p$ is an odd prime, $4 \mid…
Circulant matrices are an important tool widely used in coding theory and cryptography. A circulant matrix is a square matrix whose rows are the cyclic shifts of the first row. Such a matrix can be efficiently stored in memory because it is…
Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…
A sequence in the additive group ${\mathbb Z}_n$ of integers modulo $n$ is called $n$-zero-free if it does not contain subsequences with length $n$ and sum zero. The article characterizes the $n$-zero-free sequences in ${\mathbb Z}_n$ of…
In this paper, for an odd prime $p$ such that $p\equiv 3\bmod 4$, odd $n$, and $d=(p^n+1)/(p^k+1)+(p^n-1)/2$ with $k|n$, the value distribution of the exponential sum $S(a,b)$ is calculated as $a$ and $b$ run through $\mathbb{F}_{p^n}$. The…
A cut-down de Bruijn sequence is a cyclic string of length $L$, where $1 \leq L \leq k^n$, such that every substring of length $n$ appears at most once. Etzion [Theor. Comp. Sci 44 (1986)] gives an algorithm to construct binary cut-down de…
We present new constructions of codes for asymmetric channels for both binary and nonbinary alphabets, based on methods of generalized code concatenation. For the binary asymmetric channel, our methods construct nonlinear…
One of the most important and challenging problems in coding theory is to construct codes with best possible parameters and properties. The class of quasi-cyclic (QC) codes is known to be fertile to produce such codes. Focusing on QC codes…
The ground states of the Bernasconi model are binary +1/-1 sequences of length N with low autocorrelations. We introduce the notion of perfect sequences, binary sequences with one-valued off-peak correlations of minimum amount. If they…
Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length $2^m-1$…
Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…
LDPC codes constructed from permutation matrices have recently attracted the interest of many researchers. A crucial point when dealing with such codes is trying to avoid cycles of short length in the associated Tanner graph, i.e. obtaining…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…
There is a one-to-one correspondence between $\ell$-quasi-cyclic codes over a finite field $\mathbb F_q$ and linear codes over a ring $R = \mathbb F_q[Y]/(Y^m-1)$. Using this correspondence, we prove that every $\ell$-quasi-cyclic self-dual…