In the 1960s and 1970s the Nordstrom-Robinson-Code [30] and subsequently the infinite series of the Preparata[31], Kerdock[21], Delsarte-Goethals[6] and Goethals-Codes [7] were discovered. Apart from a few corner cases, all of these codes are non-linear binary block codes that have higher minimum distance than any known comparable (having equal size and length) linear binary code. We will call ...

In an application, where a client wants to obtain many symbols from a large database, it is often desirable to balance the load. Batch codes (introduced by Ishai et al. in STOC 2004) do exactly that: the large database is divided between many servers, so that the client has to only make a small number of queries to every server to obtain sufficient information to reconstruct all desired symbols...

We mention four recent results, none of which has appeared yet. They come from different sources. The purpose of these notes is to present them in a short way. Two results concern the generalization of the Roos-bound from cyclic codes to more general linear codes. Two others concern the use of majority coset decoding to the decoding of cyclic codes. ∗Supported by NWO, The Netherlands. Prepared ...

Minimal linear codes are linear codes such that the support of every codeword does not contain the support of another linearly independent codeword. Such codes have applications in cryptography, e.g. to secret sharing. We pursue here their study and construct asymptotically good families of minimal linear codes. We also push further the study of quasi-minimal and almost-minimal linear codes, re...

On linear q-ary completely regular codes with ρ = 2 and dual antipodal * Abstract We characterize all linear q-ary completely regular codes with covering radius ρ = 2 when the dual codes are antipodal. These completely regular codes are extensions of 1 linear completely regular codes with covering radius 1, which are all classified. For ρ = 2, we give a list of all such codes known to us. This ...

In this paper we derive a Gilbert-Varshamov type bound for linear codes over Galois rings GR(pl; j): However, this bound does not guarantee existence of better linear codes over GR(pl; j) than the usual Gilbert-Varshamov bound for linear codes over the residue class field GR(pj): Next we derive a Gilbert-Varshamov type bound for Z4 linear codes which guarantees the existence of Z4 linear codes ...