Applicable Algebra in Engineering, Communication and Computing

It is known that the following five counting problems lead to the same integer sequence $${f_t}({n})$$ f t ( n ) : (1) the number of nonequivalent compact Huffman codes of length n over an alphabet of t letters, (2) the number of “nonequivalent” …

The projective norm graphs are central objects to extremal combinatorics. They appear in a variety of contexts, most importantly they provide tight constructions for the Turán number of complete bipartite graphs $$K_{t,s}$$ K t , s with …

In 2016, Y. Kumar et al. in the paper ‘Affine equivalence and non-linearity of permutations over $${\mathbb {Z}}_n$$ Z n ’ conjectured that: For $$n\ge 3$$ n ≥ 3 , the nonlinearity of any permutation on $${\mathbb {Z}}_n$$ Z n , the ring of …

In this work, we give three new techniques for constructing Hermitian self-dual codes over commutative Frobenius rings with a non-trivial involutory automorphism using $$\lambda$$ λ -circulant matrices. The new constructions are derived as …

Let p be a prime and n be a positive integer. We consider rational functions $$f_b(X)=X+1/(X^p-X+b)$$ f b ( X ) = X + 1 / ( X p - X + b ) over $${\mathbb {F}}_{p^n}$$ F p n with $$\textrm{Tr}(b)\ne 0$$ Tr ( b ) ≠ 0 . In Hou and Sze (Finite Fields …