Motivated by questions in property testing, we search for linear error-correcting codes that have the “single local orbit” property: i.e., they are specified by a single local constraint and its translations under the symmetry group of the code. We show that the dual of every “sparse” binary code whose coordinates are indexed by elements of F2n for prime n, and whose symmetry group includes the...

Cyclic orbit codes are a family of constant dimension codes used for random network coding. We investigate the Plücker embedding of these codes and show how to efficiently compute the Grassmann coordinates of the code words.

Spread codes and orbit codes are special families of constant dimension subspace codes. These codes have been wellstudied for their error correction capability and transmission rate, but the question of how to encode messages has not been investigated. In this work we show how the message space can be chosen for a given code and how message enand decoding can be done.

We study orbit codes in the field extension $ \mathbb{F}_{q^n} $. First we show that automorphism group of a cyclic code is contained normalizer Singer subgroup if generated by subspace not proper subfield then generalize to orbits under subgroup. In situation some exceptional cases arise and open remain. Finally characterize linear isometries between such codes.

Cyclic subspace codes gained a lot of attention especially because they may be used in random network coding for correction errors and erasures. Roth, Raviv Tamo 2018 established connection between cyclic (with certain parameters) Sidon spaces. These latter objects were introduced by Bachoc, Serra Zémor 2017 relation with the linear analogue Vosper's Theorem. This allowed to construct large cla...

We construct an “orbital Tutte polynomial” associated with a dual pair M and M∗ of matrices over a principal ideal domain R and a group G of automorphisms of the row spaces of the matrices. The polynomial has two sequences of variables, each sequence indexed by associate classes of elements of R. In the case where M is the signed vertex-edge incidence matrix of a graph Γ over the ring of intege...