相关论文: Weighted external difference families and R-optima…
This paper provides a combinatorial characterization of weak algebraic manipulation detection (AMD) codes via a kind of generalized external difference families called bounded standard weighted external difference families (BSWEDFs). By…
External difference families (EDFs) are combinatorial objects which were introduced in the early 2000s, motivated by information security applications such as the construction of AMD codes. Various generalizations have since been defined…
Strong external difference families (SEDFs) have applications to cryptography and are rich combinatorial structures in their own right; until now, all SEDFs have been in abelian groups. In this paper, we consider SEDFs in both abelian and…
This paper provides a mathematical analysis of optimal algebraic manipulation detection (AMD) codes. We prove several lower bounds on the success probability of an adversary and we then give some combinatorial characterizations of AMD codes…
(Strong) circular external difference families (which we denote as CEDFs and SCEDFs) can be used to construct nonmalleable threshold schemes. They are a variation of (strong) external difference families, which have been extensively studied…
We consider strong external difference families (SEDFs); these are external difference families satisfying additional conditions on the patterns of external diferences that occur, and were first defined in the context of classifying optimal…
Strong difference families of special types are introduced to produce new relative difference families from the point of view of both asymptotic existences and concrete examples. As applications, group divisible designs of type $30^u$ with…
Strong external difference family (SEDF) and its generalizations GSEDF, BGSEDF in a finite abelian group $G$ are combinatorial designs raised by Paterson and Stinson [7] in 2016 and have applications in communication theory to construct…
We consider weighted Reed-Muller codes over point ensemble $S_1 \times...\times S_m$ where $S_i$ needs not be of the same size as $S_j$. For $m = 2$ we determine optimal weights and analyze in detail what is the impact of the ratio…
In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed-Solomon block codes to…
Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and computer science. Yet, many of their important properties are…
This paper introduces a new combinatorial construction for q-ary constant-weight codes which yields several families of optimal codes and asymptotically optimal codes. The construction reveals intimate connection between q-ary…
Weak superimposed codes are combinatorial structures related closely to generalized cover-free families, superimposed codes, and disjunct matrices in that they are only required to satisfy similar but less stringent conditions. This class…
We introduce the concept of a disjoint partial difference family (DPDF) and an external partial difference family (EPDF), a natural generalisation of the much-studied structures of disjoint difference family (DDF), external difference…
Strong external difference families (SEDFs) were introduced by Paterson and Stinson as a more restrictive version of external difference families. SEDFs can be used to produce optimal strong algebraic manipulation detection codes. We…
In this paper we expand our recently introduced concept of UW-OFDM (unique word orthogonal frequency division multiplexing). In UW-OFDM the cyclic prefixes (CPs) are replaced by deterministic sequences, the so-called unique words (UWs). The…
We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise…
Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the…
Understanding atomic structures is crucial, yet amorphous materials remain challenging due to their irregular and non-periodic nature. The Wavelet Transform Radial Distribution Function (WT-RDF) offers a physics-based framework for…
Strong external difference families (SEDFs) were introduced by Paterson and Stinson as a more restrictive version of external difference families. SEDFs can be used to produce optimal strong algebraic manipulation detection codes. In this…