Related papers: A Direct Construction of Cross Z-Complementary Seq…
One of the important applications of Golay complementary sets (GCSs) is the reduction of peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency division multiplexing (OFDM) systems. OFDM has played a major role in modern wireless…
The infinite-component Chern-Simons-Maxwell (iCSM) theory is a 3+1D generalization of the 2+1D Chern-Simons-Maxwell theory by including an infinite number of coupled gauge fields. It can be used to describe interesting 3+1D systems. In…
Maximal Common Subsequences (MCSs) between two strings X and Y are subsequences of both X and Y that are maximal under inclusion. MCSs relax and generalize the well known and widely used concept of Longest Common Subsequences (LCSs), which…
We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in $[0,\frac{1}{3}]$, answering a question of Cameron, and that the number of those…
A collection of complex sequences of length v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequence A=[a_0,a_1,...,a_{v-1}] of length v=dm we define the…
In this paper, we propose a sequence construction framework that extends prime-length Bj\"orck sequences, a class of Constant Amplitude Zero Autocorrelation (CAZAC) sequences, to arbitrary lengths using Goldbach's conjecture for even and…
For a sequence $S$ over a finite abelian group, let $MZ(S)$ denote the length of the shortest nonempty zero-sum subsequence of $S$. We prove that if $G$ is finite abelian of order $n$ and $S$ has length $n$, then $MZ(S)\le n-|\supp(S)|+1$.…
Like other pseudorandom sequences, decimal sequences may be used in designing a Code Division Multiple Access (CDMA) system. They appear to be ideally suited for this since the cross-correlation of d-sequences taken over the LCM of their…
We give the first construction of explicit constant-degree lossless vertex expanders. Specifically, for any $\varepsilon > 0$ and sufficiently large $d$, we give an explicit construction of an infinite family of $d$-regular graphs where…
Construction of signal sets with low correlation property is of interest to designers of CDMA systems. One of the preferred ways of constructing such sets is the interleaved construction which uses two sequences a and b with 2-level…
In this paper, we survey constructions of and nonexistence results on combinatorial/geometric structures which arise from unions of cyclotomic classes of finite fields. In particular, we survey both classical and recent results on…
Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of…
Compositional zero-shot learning (CZSL) aims to recognize unseen attribute-object compositions by recombining primitives learned from seen pairs. Recent CZSL methods built on vision-language models (VLMs) typically adopt parameter-efficient…
Constant dimension codes (CDCs) have become an important object in coding theory due to their application in random network coding. The multilevel construction is one of the most effective ways to construct constant dimension codes. The…
The one-dimensional (1-D) Golay complementary set (GCS) has many well-known properties and has been widely employed in engineering. The concept of 1-D GCS can be extended to the two-dimensional (2-D) Golay complementary array set (GCAS)…
We establish a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric…
Spread spectrum multiple access systems demand minimum possible cross-correlation between the sequences within a set of sequences having good auto-correlation properties. Through a connection between generalised Frank sequences and…
Compositional Zero-Shot Learning (CZSL) is a critical task in computer vision that enables models to recognize unseen combinations of known attributes and objects during inference, addressing the combinatorial challenge of requiring…
It is shown that pairs of maximal linear recursive sequences (m-sequences) typically have mean square aperiodic crosscorrelation on par with that of random sequences, but that if one takes a pair of m-sequences where one is the reverse of…
In this paper, a recent method to construct complementary sequence sets and complete complementary codes by Hadamard matrices is deeply studied. By taking the algebraic structure of Hadamard matrices into consideration, our main result…