Querying source code interactively for information is a critical task in reverse engineering of software. However, current source code query systems succeed in handling only small subsets of the wide range of queries possible on code, trading generality and expressive power for ease of implementation and practicality. We attribute this to the absence of clean formalisms for modeling and queryin...

Starting from the four DNA bases order in the Boolean lattice, a novel Lie Algebra of the genetic code is proposed. Here, the main partitions of the genetic code table were obtained as equivalent classes of quotient spaces of the genetic code vector space over the Galois field of the four DNA bases. The new algebraic structure shows strong connections among algebraic relationships, codon assign...

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear functions and planar functions over finite fields are employed to construct a number of classes of cyclic codes. Lower bounds on the minimum weight of some class...

Based on a sufficient condition proposed by Hollmann and Xiang forconstructing triple-error-correcting codes, the minimum distance of a binary cycliccodeC1,3,13 with three zeros α, α3, and α13 of length 2−1 and the weight divisibilityof its dual code are studied, where m ≥ 5 is odd and α is a primitive element of thefinite field F2m . The codeC1,3,13 is proven to hav...

SOFTWARE–HARDWARE SYSTEMS TRANSLATION OF ALGEBRAIC PROGRAMS INTO EXECUTABLE CODES S. V. Goncharov and A. Ye. Rudich UDC 519.681.3 An approach to the problem of translation of algebraic programs into executable codes is presented. In particular, an algorithm for translation of algebraic programs represented in the language Aplan into C codes is proposed. An algorithm of reconstruction of types i...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

The paper “Scrap your boilerplate” (SYB) introduces a combinator library for generic programming that offers generic traversals and queries. Classically, support for generic programming consists of two essential ingredients: a way to write (type-)overloaded functions, and independently, a way to access the structure of data types. SYB seems to lack the second. As a consequence, it is difficult ...

An infinite series of curves is constructed in order to show that all linear codes can be obtained from curves using Goppa's construction. If one imposes conditions on the degree of the divisor used, then we derive criteria for linear codes to be algebraic-geometric. In particular, we investigate the family of q-ary Hamming codes, and prove that only those with redundancy one or two, and the bi...

Ideas from algebraic geometry became useful in coding theory after Goppa’s construction [7]. He had the beautiful idea of associating to a (projective, geometrically irreducible, non-singular, algebraic) curve X defined over Fq, the finite field with q elements, a code C. This code is constructed from two divisors D and G on X , where one of them, say D, is the sum of n distinct Fq-rational poi...