The finite Grassmannian Gq(k, n) is defined as the set of all k-dimensional subspaces of the ambient space Fq . Subsets of the finite Grassmannian are called constant dimension codes and have recently found an application in random network coding. In this setting codewords from Gq(k, n) are sent through a network channel and, since errors may occur during transmission, the received words can po...

We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with $p$-faces $n$-cube (for $n>p$) and stabilizer constraints faces dimension $(p\pm1)$. The code identifying antipodal resulting complex encodes one logical qubit into $N = 2^{n-p-1} \tbinom{n}{p}$ physical displays local testability soundness $\Omega(1/\log(N))$ beating current state-of-the-art $1/\log...

Keywords: Linear codes MDS-codes AMS Subject classiication (1985) 94B05 Summary: We give several bounds for the length, dimension or minimum distance of linear block codes whose dimension equals the minimum distance of their dual codes. Zusammenfassung: Wir geben verschiedene Schranken f ur die L ange, die Dimension und den Minimalabstand linearer Blockcodes, deren Dimension gleich dem Mini-mal...