Orthogonal arrays and orthogonal partitions have great significance in communications and coding theory. In this letter, by using a generalized orthogonal partition, Latin squares and orthogonal Latin squares, we present an iterative construction method of orthogonal arrays of strength t and orthogonal partitions. As an application of the method, more orthogonal arrays of strength t and orthogonal partitions than the existing methods can be constructed.

Quantum combinatorial designs are gaining popularity in quantum information theory. Quantum Latin squares can be used to construct mutually unbiased maximally entangled bases and unitary error bases. Here we present a general method for constructing quantum Latin arrangements from irredundant orthogonal arrays. As an application of the method, many new quantum Latin arrangements are obtained. We also find a sufficient condition such that the improved quantum orthogonal arrays [10] are equivalent to quantum Latin arrangements. We further prove that an improved quantum orthogonal array can produce a quantum uniform state.

In this study, we developed a new orthogonal partition concept for asymmetric orthogonal arrays and used it for the construction of orthogonal arrays for the first time. Permutation matrices and the Kronecker product were also successfully and skillfully used as our main tools. Hence, a new general iterative construction method for asymmetric orthogonal arrays of high strength was developed, and some new infinite families of orthogonal arrays of strength 3 and several new orthogonal arrays of strength 4, 5, and 6 were obtained.

In this work, we introduce notions of quantum frequency arrangements consisting of quantum frequency squares, cubes, hypercubes and a notion of orthogonality between them. We also propose a notion of quantum mixed orthogonal array (QMOA). By using irredundant mixed orthogonal array proposed by Goyeneche et al. we can obtain k-uniform states of heterogeneous systems from quantum frequency arrangements and QMOAs. Furthermore, some examples are presented to illustrate our method.

In this paper, by using the properties of the cyclic Hadamard matrices of order 4t, an infinite class of (4t-1)-variable 2-resilient rotation symmetric Boolean functions is constructed, and the nonlinearity of the constructed functions are also studied. To the best of our knowledge, this is the first class of direct constructions of 2-resilient rotation symmetric Boolean functions. The spirit of this method is different from the known methods depending on the solutions of an equation system proposed by Du Jiao, et al. Several situations are examined, as the direct corollaries, three classes of (4t-1)-variable 2-resilient rotation symmetric Boolean functions are proposed based on the corresponding sequences, such as m sequences, Legendre sequences, and twin primes sequences respectively.

In this letter, a property of the characteristic matrix of the Rotation Symmetric Boolean Functions (RSBFs) is characterized, and a sufficient and necessary condition for RSBFs being 1st correlation-immune (1-CI for simplicity) is obtained. This property is applied to construct resilient RSBFs of order 1 (1-resilient for simplicity) on pq variables, where p and q are both prime consistently in this letter. The results show that construction and counting of 1-resilient RSBFs on pq variables are equivalent to solving an equation system and counting the solutions. At last, the counting of all 1-resilient RSBFs on pq variables is also proposed.

Bent functions have been applied to cryptography, spread spectrum, coding theory, and combinatorial design. Permutations play an important role in the design of cryptographic transformations such as block ciphers, hash functions and stream ciphers. By using the Kronecker product this paper presents a general recursive construction method of permutations over finite field. As applications of our method, several infinite classes of permutations are obtained. By means of the permutations obtained and M-M functions we construct several infinite families of bent functions.

In the theory of orthogonal arrays, an orthogonal array (OA) is called schematic if its rows form an association scheme with respect to Hamming distances. In this paper, we study the Hamming distances of any two rows in an OA, construct some schematic OAs of strength two and give the positive solution to the open problem for classifying all schematic OAs. Some examples are given to illustrate our methods.

Variable strength orthogonal array, as a special form of variable strength covering array, plays an important role in computer software testing and cryptography. In this paper, we study the construction of variable strength orthogonal arrays with strength two containing strength greater than two by Galois field and construct some variable strength orthogonal arrays with strength l containing strength greater than l by Fan-construction.

In this paper, the notion of 2-tuples distribution matrices of the rotation symmetric orbits is proposed, by using the properties of the 2-tuples distribution matrix, a new characterization of 2-resilient rotation symmetric Boolean functions is demonstrated. Based on the new characterization of 2-resilient rotation symmetric Boolean functions, constructions of 2-resilient rotation symmetric Boolean functions (RSBFs) are further studied, and new 2-resilient rotation symmetric Boolean functions with prime variables are constructed.

The orthogonal array is an important object in combinatorial design theory, and it is applied to many fields, such as computer science, coding theory and cryptography etc. This paper mainly studies the existence of the mixed orthogonal arrays of strength two with seven factors and presents some new constructions. Consequently, a few new mixed orthogonal arrays are obtained.

We present a rebound attack on the 4-branch type-2 generalized Feistel structure with an SPS round function, which is called the type-2 GFN-SPS in this paper. Applying a non-full-active-match technique, we construct a 6-round known-key truncated differential distinguisher, and it can deduce a near-collision attack on compression functions of this structure embedding the MMO or MP modes. Extending the 6-round attack, we build a 7-round truncated differential path to get a known-key differential distinguisher with seven rounds. The results give some evidences that this structure is not stronger than the type-2 GFN with an SP round function and not weaker than that with an SPSP round function against the rebound attack.