## Designs, Codes and Cryptography OnlineFirst articles

13-05-2022 | Correction

### Correction to: Dispelling myths on superposition attacks: formal security model and attack analyses

In this article the wrong figure appeared in Appendix A2; the figure should have appeared as shown below.

10-05-2022

### A note on the Assmus–Mattson theorem for some binary codes

We previously proposed the first nontrivial examples of a code having support t-designs for all weights obtained from the Assmus–Mattson theorem and having support $$t'$$ t ′ -designs for some weights with some $$t'>t$$ t ′ > t . This suggests the …

09-05-2022

### Sharper bounds on four lattice constants

The Korkine–Zolotareff (KZ) reduction and its generalisations, are widely used lattice reduction strategies in communications and cryptography. The KZ constant and Schnorr’s constant were defined by Schnorr in 1987. The KZ constant can be used to …

07-05-2022

### Optimal selection for good polynomials of degree up to five

An $$(r,\ell )$$ ( r , ℓ ) -good polynomial is a polynomial of degree $$r+1$$ r + 1 that is constant on $$\ell $$ ℓ subsets of $$\mathbb F_q$$ F q , each of size $$r+1$$ r + 1 . For any positive integer $$r\le 4$$ r ≤ 4 we provide an $$(r,\ell )$$ …

07-05-2022

### On permutation quadrinomials with boomerang uniformity 4 and the best-known nonlinearity

Motivated by recent works on the butterfly structure, particularly by its generalization introduced by Canteaut et al. (IEEE Trans Inf Theory 63(11):7575–7591, 2017), we first push further the study of permutation polynomials over binary finite …

30-04-2022

### On the automorphisms of generalized algebraic geometry codes

We consider the class of generalized algebraic geometry codes (GAG codes) formed by two collections of places, with places of the same degree in each collection. We introduce the concept of $$N_1N_2$$ N 1 N 2 -automorphism group of a GAG code in …

Open Access 27-04-2022

### On -points of q-analogs of the Fano plane

Arguably, the most important open problem in the theory of q-analogs of designs is the question regarding the existence of a q-analog D of the Fano plane. As of today, it remains undecided for every single prime power order q of the base field. A …

Open Access 21-04-2022

### High order elements in finite fields arising from recursive towers

We illustrate a general technique to construct towers of fields producing high order elements in $$\mathbb {F}_{q^{2^n}}$$ F q 2 n , for odd q, and in $$\mathbb {F}_{2^{2 \cdot 3^n}}$$ F 2 2 · 3 n , for $$n \ge 1$$ n ≥ 1 . These towers are …

20-04-2022

### An infinite family of antiprimitive cyclic codes supporting Steiner systems

Coding theory and combinatorial t-designs have close connections and interesting interplay. One of the major approaches to the construction of combinatorial t-designs is the employment of error-correcting codes. As we all known, some t-designs …

Open Access 03-03-2022

### Delandtsheer–Doyen parameters for block-transitive point-imprimitive 2-designs

Delandtsheer and Doyen bounded, in terms of the block size, the number of points of a point-imprimitive, block-transitive 2-design. To do this they introduced two integer parameters m, n, now called Delandtsheer–Doyen parameters, linking the block …

28-02-2022

### Johnson graph codes

Array codes are the preferred codes for distributed storage, such that different rows in an array are stored at different nodes. Layered codes use a sparse format for stored arrays with a single parity check per column and no other parity checks.

22-02-2022

### Decoding algorithms of monotone codes and azinv codes and their unified view

This paper investigates linear-time decoding algorithms for two classes of error-correcting codes. One of the classes is monotone codes which are known as single deletion error-correcting codes, although they are not known to be single …

31-01-2022

### New code-based cryptographic accumulator and fully dynamic group signature

A cryptographic accumulator is a cryptographic primitive which produces a succinct aggregate of a set of elements. This type of scheme allows to produce a membership proof for each element of the set. In this paper, we propose a code-based …

20-01-2022

### Construction of asymmetric Chudnovsky-type algorithms for multiplication in finite fields

The original algorithm of D.V. Chudnovsky and G.V. Chudnovsky for the multiplication in extensions of finite fields provides a bilinear complexity which is uniformly linear with respect to the degree of the extension. Recently, Randriambololona …

14-01-2022

### Approximate unitary 3-designs from transvection Markov chains

Unitary k-designs are probabilistic ensembles of unitary matrices whose first k statistical moments match that of the full unitary group endowed with the Haar measure. In prior work, we showed that the automorphism group of classical $${\mathbb …

05-01-2022

### Equidistant permutation group codes

We study permutation codes which are groups and all of whose non-identity code elements have the same number of fixed points. It follows that over certain classes of groups such permutation codes exist.

05-01-2022

### The Eckardt point configuration of cubic surfaces revisited

The classification problem for cubic surfaces with 27 lines is concerned with describing a complete set of the projective equivalence classes of such surfaces. Despite a long history of work, the problem is still open. One approach is to use a …

05-01-2022

### A new construction of linear codes with one-dimensional hull

The hull of a linear code C is the intersection of C with its dual $$C^\perp $$ C ⊥ . The hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing the automorphism group of a …

04-01-2022

### Further improvement on index bounds

In this paper we obtain further improvement of index bounds for character sums of polynomials over finite fields. We present some examples, which show that our new bound is an improved bound compared to both the Weil bound and the index bound …

23-11-2021

### -Cyclic codes over

Let $$\mathbb {F}_q$$ F q be the finite field of order $$q=p^m$$ q = p m , where p is a prime, m is a positive integer, and $$\mathcal {R}=\mathbb {F}_q[u,v]/\langle u^2-u, v^2-v, uv-vu \rangle $$ R = F q [ u , v ] / ⟨ u 2 - u , v 2 - v , u v - v …