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Designs, Codes and Cryptography OnlineFirst articles

13.10.2018

On the cylinder conjecture

In this paper, we associate a weight function with a set of points satisfying the conditions of the cylinder conjecture. Then we derive properties of this weight function using the Rédei polynomial of the point set. Using additional assumptions on …

11.10.2018

Totally decomposed cumulative Goppa codes with improved estimations

A class of q-ary totally decomposed cumulative $$\varGamma (L,G^{j})$$ Γ ( L , G j ) -codes with $$L=\{ \alpha \in :G(\alpha )\ne 0 \}$$ L = { α ∈ : G ( α ) ≠ 0 } and $$G^{j}=G^{j}(x),\; 1 \le j\le q$$ G j = G j ( x ) , 1 ≤ j ≤ q , where G(x) is a …

09.10.2018

Factorization of a class of composed polynomials

In this paper, we provide the degree distribution of irreducible factors of the composed polynomial f(L(x)) over $$\mathbb {F}_q$$ F q , where $$f(x)\in \mathbb {F}_q[x]$$ f ( x ) ∈ F q [ x ] is irreducible and $$L(x)\in \mathbb {F}_q[x]$$ L ( x ) …

09.10.2018

Improved syndrome decoding of lifted -interleaved Gabidulin codes

A syndrome decoding algorithm for lifted interleaved Gabidulin codes of order L is proposed. The algorithm corrects L times more deviations (packet insertions) than known syndrome decoding methods with probability at least $$1-8q^{-n}$$ 1 - 8 q - …

09.10.2018

Equiangular tight frames from group divisible designs

An equiangular tight frame (ETF) is a type of optimal packing of lines in a real or complex Hilbert space. In the complex case, the existence of an ETF of a given size remains an open problem in many cases. In this paper, we observe that many of …

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There is a great deal of activity in design theory, coding theory and cryptography and recently there has been considerable research done which brings together more than one of the subjects. Designs, Codes and Cryptography provides a forum for high quality papers of both a theoretical and a practical nature which bridge more than one of these areas, encouraging interaction between them. It emphasizes the algebraic and geometric aspects of design theory, coding theory and cryptography.

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