We suggest a new approach to obtain bounds on locally correctable and some locally testable binary linear codes, by arguing that these codes (or their subcodes) have coset leader graphs with high discrete Ricci curvature. The bounds we obtain for locally correctable codes are worse than the best known bounds obtained using quantum information theory, but are better than those obtained using oth...

Electric-magnetic duality and higher dimensional analogues are obtained as symmetries in generalized coset constructions, similar to the axial-vector duality of twodimensional coset models described by Roček and Verlinde. We also study global aspects of duality between p-forms and (d−p−2)-forms in d-manifolds. In particular, the modular duality anomaly is governed by the Euler character as in f...

Coset enumeration is one of the basic tools for investigating nitely presented groups. Many enumerations require signiicant resources, in terms of CPU time or memory space. We develop a fully functional parallel coset enumeration procedure and we discuss some of the issues involved in such parallelisation using the POSIX threads library. Our results can equally well be applied to any master-sla...

We derive the Green-Schwarz action on AdS 5 × S 5 using an alternate version of the coset superspace construction. By Wick rotations and Lie algebra identifications we bring the coset to GL(4|4)/(Sp(4) ⊗ GL(1)) 2 , which allows us to represent the conformal transformations on unconstrained matrices. The derivation is more streamlined even for the bosonic sector, and conformal symmetry is manife...

Here is a simplified proof that every sharply transitive subset of $\mathrm{PGL}_2(K)$ coset subgroup.