Related papers: On codes induced from Hadamard matrices
The decomposition of large unitary matrices into smaller ones is important, because it provides ways to realization of classical and quantum information processing schemes. Today, most of the methods use planar meshes of tunable two-channel…
We establish dihedral quantum codes of short block length, a class of CSS codes obtained by the lifted product construction. We present the code construction and give a formula for the code dimension, depending on the two classical codes…
We introduce frameworks for constructing global derived moduli stacks associated to a broad range of problems, bridging the gap between the concrete and abstract conceptions of derived moduli. Our three approaches are via differential…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
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…
Hermitian hulls of linear codes are interesting for theoretical and practical reasons alike. In terms of recent application, linear codes whose hulls meet certain conditions have been utilized as ingredients to construct…
There are several well-known methods that one can use to construct Hadamard matrices from base sequences BS(m,n). In view of the recent classification of base sequences BS(n+1,n) for n <= 30, it may be of interest to show on an example how…
Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
We propose a decoding algorithm for the $(u\mid u+v)$-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a non-coherent multi-shot network, where the unknown and time-variant network is used several times. In order to…
The solving of linear systems provides a rich area to investigate the use of nearer-term, noisy, intermediate-scale quantum computers. In this work, we discuss hybrid quantum-classical algorithms for skewed linear systems for…
We analyze the set of real and complex Hadamard matrices with additional symmetry constrains. In particular, we link the problem of existence of maximally entangled multipartite states of $2k$ subsystems with $d$ levels each to the set of…
Matrices with the displacement structures of circulant, Toeplitz, and Hankel types as well as matrices with structures generalizing these types are omnipresent in computations of sciences and engineering. In this paper, we present efficient…
Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper we discuss several graph-cover-based methods for deriving families of time-invariant…
Constructions of Hadamard matrices from smaller blocks is a well-known technique in the theory of real Hadamard matrices: tensoring Hadamard matrices and the classical arrays of Williamson, Ito are all procedures involving smaller order…
Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
Given a matrix over a skew field fixing the column (1,...,1)^t, we give formulas for a row vector fixed by this matrix. The same techniques are applied to give noncommutative extensions of probabilistic properties of codes.