Abstract In 1997, Hou and Langevin introduced the idea of constructing bent functions as the composition of a Boolean function with a permutation. Recently, K. Li, C. Li, T. Helleseth, and L. Qu constructed several classes of bent functions from quadratic permutations and permutations with Niho exponents. In this paper, we further investigate one of these classes of bent functions, establishing more general sufficient conditions and discussing their relationship with the class of Maiorana–McFarland bent functions.

Abstract Ovoids of the parabolic quadric Q(6, q) of $$\textrm{PG}(6,q)$$ PG ( 6 , q ) have been largely studied in the last 40 years. They can only occur if q is an odd prime power and there are two known families of ovoids of Q(6, q), the Thas-Kantor ovoids and the Ree-Tits ovoids, both for q a power of 3. It is well known that to any ovoid of Q(6, q) two polynomials $$f_1(X,Y,Z)$$ f 1 ( X , Y , Z ) , $$f_2(X,Y,Z)$$ f 2 ( X , Y , Z ) can be associated. In this paper we classify ovoids of Q(6, q) with $$\max \{\deg (f_1),\deg (f_2)\}<(\frac{1}{6.3}q)^{\frac{3}{13}}-1$$ max { deg ( f 1 ) , deg ( f 2 ) } < ( 1 6.3 q ) 3 13 - 1 .

Abstract We investigate APN functions which can be represented as rational functions and we provide non-existence results exploiting the connection between these functions and specific algebraic varieties over finite fields. This approach allows to classify families of functions when previous approaches cannot be applied.

Abstract. Strong blocking sets and their counterparts, minimal codes, have attracted much attention in the past few years. Combining the concatenating construction of codes with a geometric insight into the minimality condition, we explicitly provide infinite families of small strong blocking sets, whose size is linear in the dimension of the ambient projective spaces. As a byproduct, small saturating sets are obtained.

Scattered polynomials of a given index over finite fields are intriguing rare objects with many connections within mathematics. Of particular interest are the exceptional ones, as defined in 2018 by the first author and Zhou, for which partial classification results are known. In this paper we propose a unified algebraic description of$\mathbb {F}_{q^{n}}$-linear maximum rank distance codes, introducing the notion of exceptional linear maximum rank distance codes of a given index. Such a connection naturally extends the notion of exceptionality for a scattered polynomial in the rank metric framework and provides a generalization of Moore sets in the monomial MRD context. We move towards the classification of exceptional linear MRD codes, by showing that the ones of index zero are generalized Gabidulin codes and proving that in the positive index case the code contains an exceptional scattered polynomial of the same index.

This work presents a comparison of microwave radiometer (MWR) and sun-photometer integrated water vapor (IWV) data using global navigation satellite system (GNSS) IWV as reference in Portugal (2003–2021). A very high correlation is obtained for both instruments, although MWR shows a wet bias and sun-photometers, a dry one. In addition, a dependence of mean bias error (MBE) and standard deviation (SD) on IWV has been observed, increasing as IWV increases.

A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we have δ non-overlapping subsets of cardinality ri that can be used to recover the missing coordinate we say that a linear code C with length n, dimension k, minimum distance d has (r1, . . . , rδ)locality and denote by [n, k, d; r1, r2, . . . , rδ]. In this paper we provide a new upper bound for the minimum distance of these codes. Working with a finite number of subgroups of cardinality ri+ 1 of the automorphism group of a function field F|Fqof genus g ≥ 1 we propose a construction of [n, k, d; r1, r2, . . . , rδ]-codes and apply the results to some well known families of function fields.

In this paper, we generalize constructions in two recent works of Ding, Heng, and Zhou to any field Fq, q odd, providing infinite families of minimal codes for which the Ashikhmin-Barg bound does not hold.

For a linear maximum distance separable (MDS) code with redundancy r, the covering radius is either r or r -1. However, for r > 3, few examples of q-ary linear MDS codes with radius r -1 are known, including the Reed-Solomon codes with length q + 1. In this paper, for redundancies r as large as 12√q, infinite families of q-ary MDS codes with covering radius r - 1 and length less than q + 1 are constructed. These codes are obtained from algebraic-geometric codes arising from elliptic curves. For most pairs (r, q) with r ≤ 12√q, these are the shortest q-ary MDS codes with covering radius r - 1.