Related papers: Some complementary Gray codes
Each positive increasing integer sequence $\{a_n\}_{n\geq 0}$ can serve as a numeration system to represent each non-negative integer by means of suitable coefficient strings. We analyse the case of $k$-generalized Fibonacci sequences…
We study additive quaternary codes whose parameters are close to those of the extended cyclic [12; 6; 6]4-code or to the quaternary linear codes generated by the elliptic quadric in PG(3; 4) or its dual. In particular we characterize those…
The idea of (combinatorial) Gray codes is to list objects in question in such a way that two successive objects differ in some pre-specified small way. In this paper, we utilize beta-description trees to cyclicly Gray code three classes of…
A combinatorial Gray code for a set of combinatorial objects is a sequence of all combinatorial objects in the set so that each object is derived from the preceding object by changing a small part. In this paper we design a Gray code for…
In this paper we introduce a natural mathematical structure derived from Samuel Beckett's play "Quad". We call this structure a binary Beckett-Gray code. We enumerate all codes for $n \leq 6$ and give examples for $n=7,8$. Beckett-Gray…
A binary partition of a positive integer $n$ is a partition of $n$ in which each part has size a power of two. In this note we first construct a Gray sequence on the set of binary partitions of $n$. This is an ordering of the set of binary…
We show that there are good long binary generalized quasi-cyclic self-dual (either Type I or Type II) codes.
We consider two shellings of the boundary of the hypercube equivalent if one can be transformed into the other by an isometry of the cube. We observe that a class of indecomposable permutations, bijectively equivalent to standard double…
We study skew-tolerant Gray codes, which are Gray codes in which changes in consecutive codewords occur in adjacent positions. We present the first construction of asymptotically non-vanishing skew-tolerant Gray codes, offering an…
We give a complete classification of binary linear complementary dual codes of lengths up to $13$ and ternary linear complementary dual codes of lengths up to $10$.
We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on…
Linear code with complementary dual($LCD$) are those codes which meet their duals trivially. In this paper we will give rather alternative proof of Massey's theorem\cite{Massey2}, which is one of the most important characterization of $LCD$…
Binary self-dual sequences have been considered and analyzed throughout the years, and they have been used for various applications. Motivated by a construction for single-track Gray codes, we examine the structure and recursive…
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study the largest minimum weight $d(n,k)$ among all binary linear complementary dual $[n,k]$ codes. We…
Linear complementary dual codes (LCD) are linear codes satisfying $C\cap C^{\perp}=\{0\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal…
The main aim of this paper is to study $LCD$ codes. Linear code with complementary dual($LCD$) are those codes which have their intersection with their dual code as $\{0\}$. In this paper we will give rather alternative proof of Massey's…
Let C be an additive subgroup of $\Z_{2k}^n$ for any $k\geq 1$. We define a Gray map $\Phi:\Z_{2k}^n \longrightarrow \Z_2^{kn}$ such that $\Phi(\codi)$ is a binary propelinear code and, hence, a Hamming-compatible group code. Moreover,…
The results of J. F. Qiann et al. [4] on $(1-\gamma)$-cyclic codes over finite chain rings of nilpotency index 2 are extended to $(1-\gamma^e)$-cyclic codes over finite chain rings of arbitrary nilpotency index $e+1$. The Gray map is…
The $\Z_{2^s}$-additive codes are subgroups of $\Z^n_{2^s}$, and can be seen as a generalization of linear codes over $\Z_2$ and $\Z_4$. A $\Z_{2^s}$-linear code is a binary code which is the Gray map image of a $\Z_{2^s}$-additive code. We…
Recently, simplicial complexes are used in constructions of several infinite families of minimal and optimal linear codes by Hyun {\em et al.} Building upon their research, in this paper more linear codes over the ring $\mathbb{Z}_4$ are…