Related papers: Group Symmetries of Complementary Code Matrices

Topologies of large deformation Contact-aided Compliant Mechanisms (CCMs), with self and mutual contact, exemplified via path generation applications, are designed using the continuum synthesis approach. Design domains are parameterized…

A major drawback of orthogonal frequency division multiplexing (OFDM) systems is their high peak-to-mean envelope power ratio (PMEPR). The PMEPR problem can be solved by adopting large codebooks consisting of complementary sequences with…

We systematically investigate general forms of mass matrices for three-generation up and down quarks, including asymmetrical ones in generation space. Viable zero matrix elements are explored which are compatible with the current…

Constant-dimension subspace codes (CDCs), a special class of subspace codes, have attracted significant attention due to their applications in network coding. A fundamental research problem of CDCs is to determine the maximum number of…

A matrix $T \in \M_n(\C)$ is \emph{UECSM} if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We develop several techniques for studying this property in dimensions three and four. Among other things, we…

Previously, we have presented a framework to use the para-unitary (PU) matrix-based approach for constructing new complementary sequence set (CSS), complete complementary code (CCC), complementary sequence array (CSA), and complete…

This article studies one-generator and two-generator quasi-cyclic codes over finite fields. We present two versions of necessary and sufficient conditions for the symplectic selforthogonality of one-generator quasi-cyclic codes, using both…

Linear codes with complementary duals are linear codes whose intersection with their duals are trivial, shortly named LCD codes. In this paper we outline a construction for LCD codes over finite fields of order $q$ using weighing matrices…

We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. Here, the spatial symmetries of the one-dimensional…

We developed computer algebra tools for enumerating conjugacy classes of independent subsets and generating sets of symmetric groups up to $n=7$, and carried out an initial analysis of the obtained results.

The construction of complementary sets (CSs) of sequences with different set size and sequence length become important due to its practical application for OFDM systems. Most of the constructions of CSs, based on generalized Boolean…

A simple specific pattern of the two 3 X 3 quark mass matrices is proposed, resulting in a prediction of the CP phase of the charged-current mixing matrix V_CKM, i.e. sin 2 phi_1 (beta) = 0.733, which is in remarkable agreement with data,…

Group synchronization plays a crucial role in global pipelines for Structure from Motion (SfM). Its formulation is nonconvex and it is faced with highly corrupted measurements. Cycle consistency has been effective in addressing these…

We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as well as to say when some thin groups cannot be conjugate to…

Linear complementary pairs (LCPs) of codes have been studied since they were introduced in the context of discussing mitigation measures against possible hardware attacks to integrated circuits. In this situation, the security parameters…

We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…

For a pair of given binary perfect codes C and D of lengths t and m respectively, the Mollard construction outputs a perfect code M(C,D) of length tm + t + m, having subcodes C1 and D2, that are obtained from codewords of C and D…

Let $n=2^k-1$ and $m=2^{k-2}$ for a certain $k\ge 3$. Consider the point-line geometry of $2m$-element subsets of an $n$-element set. Maximal singular subspaces of this geometry correspond to binary simplex codes of dimension $k$. For $k\ge…

A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…

In this paper, we construct a symmetric group ${\rm Sym}_{2(4^n-1)}$, which contains a subgroup isomorphic to the $n$-qubit projective Clifford group $\mathcal{C}_n$. To establish this result, we investigate the centralizers of the $z$ gate…