https://faculty.nps.edu/pstanica/research/rcrot3pg.pdf

Rotation symmetric Boolean functions-Count and cryptographic properties

Two classes of permutation polynomials over finite fields

We consider the Goldberg-Coxeter construction $GC_{k,l}(G_0)$ (a generalization of a simplicial subdivision of the dodecahedron considered by Goldberg [Tohoku Mathematical Journal, 43 (1937) 104–108] and Coxeter [A Spectrum of Mathematics, OUP, (1971) 98–107]), which produces a plane graph from any $3$- or $4$-valent plane graph for integer parameters $k,l$. A zigzag in a plane graph is a circuit of edges, such that any two, but no three, consecutive edges belong to the same face; a central circuit in a $4$-valent plane graph $G$ is a circuit of edges, such that no two consecutive edges belong to the same face. We study the zigzag (or central circuit) structure of the resulting graph using the algebraic formalism of the moving group , the $(k,l)$-product and a finite index subgroup of $SL_2(\Bbb{Z})$, whose elements preserve the above structure. We also study the intersection pattern of zigzags (or central circuits) of $GC_{k,l}(G_0)$ and consider its projections , obtained by removing all but one zigzags (or central circuits).

/pdf/goldberg-coxeter-construction-for-3-and-4-valent-plane-uzh4rn5hwm.pdf

Goldberg-Coxeter Construction for $3$- and $4$-valent Plane Graphs

We consider deletion channels and insertion channels under an additional segmentation assumption: the input consists of disjoint segments of b consecutive bits, with at most one error per segment. Under this assumption, we demonstrate simple and computationally efficient deterministic encoding and decoding schemes that achieve a high provable rate even under worst-case errors. We also consider more complex schemes that experimentally achieve higher rates under random error.

/pdf/codes-for-deletion-and-insertion-channels-with-segmented-1y4a1pfevf.pdf

Codes for Deletion and Insertion Channels with Segmented Errors

We consider deletion channels and insertion channels under an additional segmentation assumption: the input consists of disjoint segments of b consecutive bits, with at most one error per segment. Under this assumption, we demonstrate simple and computationally efficient deterministic encoding and decoding schemes that achieve a high provable rate even under worst case errors. We also consider more complex schemes that experimentally achieve higher rates under random error.

/pdf/codes-for-deletion-and-insertion-channels-with-segmented-2owapef81i.pdf

Ákoss Seress

Papers

On single-deletion-correcting codes

Geometry, codes and difference sets: exceptional connections

Face-regular polyhedra and tilings with two combinatorial types of faces

Decoding some doubly-even self-dual [32, 16, 8] codes by hand

A mass formula for Type II codes over finite fields of characteristic two