In the construction of cryptosystems, we need functions with some cryptographically significant properties. It is known that the Global Avalanche Characteristic (GAC) is one of them, which is based on the correlation of functions. In this paper …

DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization of its nucleotides. The formation of large stem-length secondary structures makes the sequences chemically inactive towards …

This article introduces the concept of $$\mathcal {S}_0$$ S 0 -equivalence class, i.e. , n-variable Boolean functions up to the addition of a symmetric function null in $$0_n$$ 0 n and $$1_n$$ 1 n , and investigates its application to study …

Code-based cryptography received attention after the NIST started the post-quantum cryptography standardization process in 2016. A central NP-hard problem is the binary syndrome decoding problem, on which the security of many code-based …

Additive codes have a wide range of applications. A classical nice and generic way to construct linear codes is via trace functions. In this paper, first, we generalize this method to construct additive codes. Then, we use this method to get some …

In recent years, zero-correlation zone (ZCZ) sequences have been studied due to their significant applications in quasi-synchronous code division multiple access (QS-CDMA) systems and other wireless communication domains. However, in a cognitive …

V. Levenshtein first proposed the sequence reconstruction problem in 2001. This problem studies the same sequence from some set is transmitted over multiple channels, and the decoder receives the different outputs. Assume that the transmitted …

Additive codes have gained importance in algebraic coding theory due to their applications in quantum error correction and quantum computing. The article begins by developing some properties of Additive Complementary Dual (ACD) codes with respect …

Many modern cryptographic primitives for hashing and (authenticated) encryption make use of constructions that are instantiated with an iterated cryptographic permutation that operates on a fixed-width state consisting of an array of bits. Often …

We describe the computer-aided classification of equitable partitions of the 12-cube with quotient matrix [[2, 10], [6, 6]], or, equivalently, simple orthogonal arrays OA(1536, 12, 2, 7), or order-7 correlation-immune Boolean functions in 12 …

This paper presents a class of integer codes that are suitable for use in various optical networks. The presented codes are generated with the help of a computer and have the ability to correct l-bit burst errors corrupting one b-bit byte …

For an (imaginary) hyperelliptic curve $$\mathcal {H}$$ H of genus g, with a Weierstrass point $$\Omega $$ Ω , taken as the point at infinity, we determine a basis of the Riemann-Roch space $$\mathcal {L}(\Delta + m \Omega )$$ L ( Δ + m Ω ) …

Differential-linear cryptanalysis is an efficient cryptanalysis method to attack ARX ciphers, which have been used to present the best attacks on many ARX primitives such as Chaskey and Chacha. In this paper, we present the differential-linear …

Bent functions have a number of practical applications in cryptography, coding theory, and other fields. Fourier transform is a key tool to study bent functions on finite abelian groups. Using Fourier transforms, in this paper, we first present …

This paper studies Abelian and consta-Abelian polyadic codes over rings defined as affine algebras over chain rings. For this purpose, we use the classical construction via splittings and multipliers of the underlying Abelian group. We also derive …

Let $$\mathbb {F}_q$$ F q be a finite field with q elements, where q is a power of a prime p. In this paper, we obtain an improvement on Weil bounds for character sums associated to a polynomial f(x) over $$\mathbb {F}_q $$ F q , which extends the …

In this paper, we not only give the parity check matrix of the [1, 0]-twisted generalized Reed-Solomon (in short, TGRS) code, but also determine the weight distribution. Especially, we show that the [1, 0]-TGRS code is not GRS or EGRS.

The sequence pairs of length $$2^{m}$$ 2 m projected from Type-II and Type-III/II complementary array pairs of size $$2\times 2\times \cdots \times 2$$ 2 × 2 × ⋯ × 2 (m-times) form Type-II and Type-III complementary sequence pairs, respectively.

In this paper, we address an open problem posed by Bai and Xia in [2]. We study polynomials of the form $$f(x)=x^{4q+1}+\lambda _1x^{5q}+\lambda _2x^{q+4}$$ f ( x ) = x 4 q + 1 + λ 1 x 5 q + λ 2 x q + 4 over the finite field $${\mathbb …

Cyclic codes are an important subclass of linear codes, they not only have good algebraic structure, but also are easy to be encoded and decoded. At present, researchers have constructed many optimal ternary cyclic codes, but the study on quinary …