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Applicable Algebra in Engineering, Communication and Computing OnlineFirst articles

19.01.2019 | Original Paper

n-dimensional optical orthogonal codes, bounds and optimal constructions

We generalize to higher dimensions the notions of optical orthogonal codes. We establish upper bounds on the capacity of general n-dimensional OOCs, and on ideal codes (codes with zero off-peak autocorrelation). The bounds are based on the Johnson …

02.01.2019 | Original Paper

Conditions for confluence of innermost terminating term rewriting systems

This paper presents a counterexample for the open conjecture whether innermost joinability of all critical pairs ensures confluence of innermost terminating term rewriting systems. We then show that innermost joinability of all normalized …

02.01.2019 | Original Paper

A Swan-like note for a family of binary pentanomials

In this note, we employ the techniques of Swan (Pac J Math 12(3):1099–1106, 1962) with the purpose of studying the parity of the number of the irreducible factors of the penatomial $$X^n+X^{3s}+X^{2s}+X^{s}+1\in \mathbb {F}_2[X]$$ X n + X 3 s + X …

01.01.2019 | Original Paper

New quadratic bent functions in polynomial forms with coefficients in extension fields

In this paper, we first discuss the bentness of a large class of quadratic Boolean functions in polynomial form $$f(x)=\sum _{i=1}^{{n}/{2}-1}\mathrm {Tr}^n_1(c_ix^{1+2^i})+ \mathrm {Tr}_1^{n/2}(c_{n/2}x^{1+2^{n/2}})$$ f ( x ) = ∑ i = 1 n / 2 - 1 …

21.11.2018 | Original Paper

Counting extended irreducible Goppa codes

We obtain an upper bound on the number of extended irreducible q-ary Goppa codes of degree r and length $$q^n+1$$ q n + 1 , where $$q=p^t$$ q = p t and n and $$r>2$$ r > 2 are prime numbers.

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Applicable Algebra in Engineering, Communication and Computing publishes mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Coverage includes vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology.

The journal offers papers dealing with problems in commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, among others.

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