Related papers: Low Correlation Sequences from Linear Combinations…
The autocorrelation values of two classes of binary sequences are shown to be good in [6]. We study the 2-adic complexity of these sequences. Our results show that the 2-adic complexity of such sequences is large enough to resist the attack…
The wayward quality of continuous prompts stresses the importance of their interpretability as unexpected and unpredictable behaviors appear following training, especially in the context of large language models automating people-sensitive…
We study the relationship between two measures of pseudorandomness for families of binary sequences: family complexity and cross-correlation measure introduced by Ahlswede et al.\ in 2003 and recently by Gyarmati et al., respectively. More…
Due to wide applications of binary sequences with low correlation to communications, various constructions of such sequences have been proposed in literature. However, most of the known constructions via finite fields make use of the…
We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a…
The coefficient sequences of multivariate rational functions appear in many areas of combinatorics. Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic properties, and the field of analytic combinatorics in several…
The generalized binary sequences of order 2 have been used to construct good binary cyclic codes [4]. The linear complexity of these sequences has been computed in [2]. The autocorrelation values of such sequences have been determined in…
The asymptotic critical exponent measures for a sequence the maximum repetition rate of factors of growing length. The infimum of asymptotic critical exponents of sequences of a certain class is called the asymptotic repetition threshold of…
Pseudorandom number generators are required to generate pseudorandom numbers which have good statistical properties as well as unpredictability in cryptography. An m-sequence is a linear feedback shift register sequence with maximal period…
When linear regression generates a relationship between a (dependent) scalar response and one or multiple independent variables, various datasets providing distinct graphical trends can develop resembling relationships based on the same…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…
A characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this…
This paper proposes a new class of random sequences called binary primes tableau (PT) sequences that have potential applications in cryptography and communications. The PT sequence of rank p is obtained from numbers arranged in a tableau…
In this paper, given a simple linear recurrence sequence of algebraic numbers, which has either a dominant characteristic root or exactly two characteristic roots of maximal modulus, we give some explicit lower bounds for the index beyond…
Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realised by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free…
Neural sequence-to-sequence models are currently the dominant approach in several natural language processing tasks, but require large parallel corpora. We present a sequence-to-sequence-to-sequence autoencoder (SEQ^3), consisting of two…
The stream of words produced by Automatic Speech Recognition (ASR) systems is typically devoid of punctuations and formatting. Most natural language processing applications expect segmented and well-formatted texts as input, which is not…
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…
In this paper, we prove new relations between the bias of multilinear forms, the correlation between multilinear forms and lower degree polynomials, and the rank of tensors over $GF(2)= \{0,1\}$. We show the following results for…
Sequences with good randomness properties are quite important for stream ciphers. In this paper, a new class of quaternary sequences is constructed by using generalized cyclotomic classes of $\mathbb{Z}_{2p^m}$ $(m\geq1)$. The exact values…