相关论文: Constructions of Polyphase Golay Complementary Arr…
In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction…
Weighted sums of left and right hand Kronecker products of Integer Sequence Doubly Affine (ISDA) as well as Generalized Arithmetic Progression Doubly Affine (GAPDA) arrays are used to generate larger ISDA arrays of multiplicative order…
The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of…
In this paper, we propose a direct construction of a novel type of code set, which has combined properties of complete complementary code (CCC) and zero-correlation zone (ZCZ) sequences and called it complete complementary-ZCZ (CC-ZCZ) code…
In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on.…
We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions…
We present a general algorithm for generating arbitrary standard complementary pairs of sequences (including binary, polyphase, M-PSK and QAM) of length 2^N using Boolean functions. The algorithm follows our earlier paraunitary algorithm,…
Macaulay Duality, between quotients of a polynomial ring over a field, annihilated by powers of the variables, and finitely generated submodules of the ring's graded dual, is generalized over any Noetherian ring, and used to provide…
Quaternary code (QC) designs form an attractive class of nonregular factorial fractions. We develop a complementary set theory for characterizing optimal QC designs that are highly fractionated in the sense of accommodating a large number…
Macaulay's Inverse System gives an effective method to construct Artinian Gorenstein k-algebras. To date a general structure for Gorenstein k-algebras of any dimension (and codimension) is not understood. In this paper we extend Macaulay's…
The Goppa Code Distinguishing (GD) problem asks to distinguish efficiently a generator matrix of a Goppa code from a randomly drawn one. We revisit a distinguisher for alternant and Goppa codes through a new approach, namely by studying the…
The modular design of planar phased array antennas with hexagonal apertures is addressed by means of innovative diamond-shaped tiling techniques. Both tiling configuration and subarray coefficients are optimized to fit user-defined…
We introduce a special class of convex rational polyhedral cones which allows to construct generalized Calabi-Yau varieties of dimension $(d + 2(r-1))$, where $r$ is a positive integer and d is the dimension of critical string vacua with…
We provide a complete enumeration of all complex Golay pairs of length up to 25, verifying that complex Golay pairs do not exist in lengths 23 and 25 but do exist in length 24. This independently verifies work done by F. Fiedler in 2013…
We present five new infinite families of linear near-MDS codes uniformly packed in the wide sense (UPWS). These codes are also almost perfect multiple coverings of the deep holes or farthest-off points (APMCF), i.e.\ the vectors lying at…
A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…
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…
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…
Sequences with good correlation properties have been widely adopted in modern communications, radar and sonar applications. In this paper, we present our new findings on some constructions of single $H$-ary Golay sequence and $4^q$-QAM…