Related papers: On binary codes related to mutually quasi-unbiased…
In this paper, code decompositions (a.k.a. code nestings) are used to design binary polarization kernels. The proposed kernels are in general non-linear. They provide a better polarization exponent than the previously known kernels of the…
Minimal codes are a class of linear codes which gained interest in the last years, thanks to their connections to secret sharing schemes. In this paper we provide the weight distribution and the parameters of families of minimal codes…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
We give a characterization for the binary linear constant weight codes by using the symmetric difference of the supports of the codewords. This characterization gives a correspondence between the set of binary linear constant weight codes…
Maximal sets of mutually unbiased bases are useful throughout quantum physics, both in a foundational context and for applications. To date, it remains unknown if complete sets of mutually unbiased bases exist in Hilbert spaces of…
Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…
This paper introduces a new combinatorial construction for q-ary constant-weight codes which yields several families of optimal codes and asymptotically optimal codes. The construction reveals intimate connection between q-ary…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…
We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length 3\ell with the algebraic approach of [9]. In particular, we improve the previous results by…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
In this paper, we study one-Lee weight and two-Lee weight codes over $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$, where $u^{2}=0$. Some properties of one-Lee weight $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-additive codes are given, and a complete…
In this work, quadratic reside codes over the ring F2 +uF2 +u^2F2 with u^3 = u are considered. A duality and distance preserving Gray map from F2 + uF2 + u^2F2 to (F_2)^3 is defined. By using quadratic double circulant, quadratic bordered…
We provide a classification method of weighing matrices based on a classification of self-orthogonal codes. Using this method, we classify weighing matrices of orders up to 15 and order 17, by revising some known classification. In…
Recently, there has been intensive research on the weight distributions of cyclic codes. In this paper, we compute the weight distributions of three classes of cyclic codes with Niho exponents. More specifically, we obtain two classes of…
We introduce quaternary modified four $\mu$-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four $\mu$-circulant Hermitian self-dual codes. We also construct quaternary modified…
Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight $d_2(n,k)$ among all binary LCD $[n,k]$ codes and the largest minimum weight $d_3(n,k)$ among all…
We show that there are good long binary generalized quasi-cyclic self-dual (either Type I or Type II) codes.
Consider the identification (ID) via channels problem, where a receiver wants to decide whether the transmitted identifier is its identifier, rather than decoding the identifier. This model allows to transmit identifiers whose size scales…
Perfect codes are arguably the most fascinating structures in combinatorial coding theory, and their classification and weight distribution are of considerable interest. This classification also involves the analysis of some related…