Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn q-ary codes with two distances d and d+1
75
0
0.0
(
0
)
Added by
Peter Boyvalenkov
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The $q$-ary block codes with two distances $d$ and $d+1$ are considered. Several constructions of such codes are given, as in the linear case all codes can be obtained by a simple modification of linear equidistant codes. Upper bounds for the maximum cardinality of such codes is derived. Tables of lower and upper bounds for small $q$ and $n$ are presented.
rate research
Read More
Lattices have been used in several problems in coding theory and cryptography. In this paper we approach $q$-ary lattices obtained via Constructions D, $D$ and $overline{D}$. It is shown connections between Constructions D and $D$. Bounds for the minimum $l_1$-distance of lattices $Lambda_{D}$, $Lambda_{D}$ and $Lambda_{overline{D}}$ and, under certain conditions, a generator matrix for $Lambda_{D}$ are presented. In addition, when the chain of codes used is closed under the zero-one addition, we derive explicit expressions for the minimum $l_1$-distances of the lattices $Lambda_{D}$ and $Lambda_{overline{D}}$ attached to the distances of the codes used in these constructions.
This paper is devoted to sequences and focuses on designing new two-dimensional (2-D) Z-complementary array pairs (ZCAPs) by exploring two promising approaches. A ZCAP is a pair of 2-D arrays, whose 2-D autocorrelation sum gives zero value at all time shifts in a zone around the $(0,0)$ time shift, except the $(0,0)$ time shift. The first approach investigated in this paper uses a one-dimensional (1-D) Z-complementary pair (ZCP), which is an extension of the 1-D Golay complementary pair (GCP) where the autocorrelations of constituent sequences are complementary within a zero correlation zone (ZCZ). The second approach involves directly generalized Boolean functions (which are important components with many applications, particularly in (symmetric) cryptography). Along with this paper, new construction of 2-D ZCAPs is proposed based on 1-D ZCP, and direct construction of 2-D ZCAPs is also offered directly by 2-D generalized Boolean functions. Compared to existing constructions based on generalized Boolean functions, our proposed construction covers all of them. ZCZ sequences are a class of spreading sequences having ideal auto-correlation and cross-correlation in a zone around the origin. In recent years, they have been extensively studied due to their crucial applications, particularly in quasi-synchronous code division multiple access systems. Our proposed 2-D ZCAPs based on 2-D generalized Boolean functions have larger 2-D $mathrm{ZCZ}_{mathrm{ratio}}=frac{6}{7}$. Compared to the construction based on ZCPs, our proposed 2-D ZCAPs also have the largest 2-D $mathrm{ZCZ}_{mathrm{ratio}}$.
BCH codes are an interesting class of cyclic codes due to their efficient encoding and decoding algorithms. In many cases, BCH codes are the best linear codes. However, the dimension and minimum distance of BCH codes have been seldom solved. Until now, there have been few results on BCH codes over $gf(q)$ with length $q^m+1$, especially when $q$ is a prime power and $m$ is even. The objective of this paper is to study BCH codes of this type over finite fields and analyse their parameters. The BCH codes presented in this paper have good parameters in general, and contain many optimal linear codes.
We study the $k$-error linear complexity of subsequences of the $d$-ary Sidelnikov sequences over the prime field $mathbb{F}_{d}$. A general lower bound for the $k$-error linear complexity is given. For several special periods, we show that these sequences have large $k$-error linear complexity.
For any integer $rho geq 1$ and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d=3 and with covering radius $rho$ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius $rho$, which are not completely regular, is also given. In both constructions the Kronecker product is the basic tool that has been used.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
