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## Applicable Algebra in Engineering, Communication and Computing OnlineFirst articles

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.

10-11-2018 | Original Paper

### Approximately -semigroups in proximal relator spaces

This article introduces approximately $$\varGamma$$ Γ -semigroups, approximately $$\varGamma$$ Γ -ideals and approximately upper $$\varGamma$$ Γ -ideals in proximal relator spaces. Some properties of descriptively approximations are …