Advances in Mathematics of Communications (AMC) publishes original research papers of the highest quality in all areas of mathematics and computer science which are relevant to applications in communications technology. For this reason, submissions from many areas of mathematics are invited, provided these show a high level of originality, new techniques, an innovative approach, novel methodologies, or otherwise a high level of depth and sophistication. Any work that does not conform to these standards will be rejected.
Areas covered include coding theory, cryptology, combinatorics, finite geometry, algebra and number theory, but are not restricted to these. This journal also aims to cover the algorithmic and computational aspects of these disciplines. Hence, all mathematics and computer science contributions of appropriate depth and relevance to the above mentioned applications in communications technology are welcome.
More detailed indication of the journal's scope is given by the subject interests of the members of the board of editors.
All papers will undergo a thorough peer reviewing process unless the subject matter of the paper does not fit the journal; in this case, the author will be informed promptly. Every effort will be made to secure a decision in three months and to publish accepted papers within six months.
- AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
- Publishes 4 issues a year in February, May, August and November.
- Publishes online only.
- Indexed in Science Citation Index E, CompuMath Citation Index, Current Contents/Physics, Chemical, & Earth Sciences, INSPEC, Mathematical Reviews, MathSciNet, PASCAL/CNRS, Scopus, Web of Science, Zentralblatt MATH and dblp: computer science bibliography.
- Archived in Portico and CLOCKSS.
- Shandong University is a founding institution of AMC.
- AMC is a publication of the American Institute of Mathematical Sciences. All rights reserved.
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Recently, several striking advances have taken place regarding the discrete logarithm problem (DLP) in finite fields of small characteristic, despite progress having remained essentially static for nearly thirty years, with the best known algorithms being of subexponential complexity. In this expository article we describe the key insights and constructions which culminated in two independent quasi-polynomial algorithms. To put these developments into both a historical and a mathematical context, as well as to provide a comparison with the cases of so-called large and medium characteristic fields, we give an overview of the state-of-the-art algorithms for computing discrete logarithms in all finite fields. Our presentation aims to guide the reader through the algorithms and their complexity analyses ab initio.
We present an application of Hilbert quasi-polynomials to order domains, allowing the effective check of the second order-domain condition in a direct way. We also provide an improved algorithm for the computation of the related Hilbert quasi-polynomials. This allows to identify order domain codes more easily.
As an optimal combinatorial object, bent functions have been an interesting research object due to their important applications in cryptography, coding theory, and sequence design. The characterization and construction of bent functions are challenging problems in general. The objective of this paper is to present a construction of p-ary weakly regular bent functions from known weakly regular bent functions. This generalizes some earlier constructions of Boolean bent functions and p-ary bent functions, and produces several infinite families of p-ary weakly regular bent functions from known ones. Some infinite families of p-ary rotation symmetric bent functions are obtained as well.
We generalize the construction of locally recoverable codes on algebraic curves given by Barg, Tamo and Vlăduţ [
We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of these codes. As a result, we find some non-equivalent completely regular codes, over the same finite field, with the same parameters and intersection array. We also study when the extension of these codes gives completely regular codes. Some of these new codes are completely transitive.
In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple pairwise balanced designs are useful in constructing other types of super-simple designs which can be applied to codes and designs. In this paper, the super-simple pairwise balanced designs with block sizes 3 and 4 are investigated and it is proved that the necessary conditions for the existence of a super-simple
We investigate a family of codes called quasi-quadratic residue (QQR) codes. We are interested in these codes mainly for two reasons: Firstly, they have close relations with hyperelliptic curves and Goppa's Conjecture, and serve as a strong tool in studying those objects. Secondly, they are very good codes. Computational results show they have large minimum distances when
Our studies focus on the weight distributions of these codes. We will prove a new discovery about their weight polynomials, i.e. they are divisible by
Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHS sets with optimal partial Hamming correlation. We present several direct constructions for balanced nested cyclic difference packings (BNCDPs) and balanced nested cyclic relative difference packings (BNCRDPs) by using trace functions and discrete logarithm. We also show three recursive constructions for FHS sets with partial Hamming correlation, which are based on cyclic difference matrices and discrete logarithm. Combing these BNCDPs, BNCRDPs and three recursive constructions, we obtain infinitely many new strictly optimal FHS sets with respect to the Peng-Fan bounds.
We generalize the code constructed recently by Wang et al, and obtain many classes of codes with a few weights. The weight distribution of these codes is completely determined, and the minimum distance of the duals of these codes is determined. We also show that some subclasses of the duals of these codes are optimal. Furthermore, some parameters of the generalized Hamming weight of these codes are calculated in certain cases.
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