Block codes, which correct asymmetric errors with limited-magnitude, are studied. These codes have been applied recently for error correction in flash memories. The codes will be represented by lattices and the constructions will be based on a generalization of Sidon sequences. In particular we will consider perfect codes for these type of errors.

Subsystem codes are a generalization of noiseless subsystems, decoherence free subspaces, and quantum error-correcting codes. We prove a Singleton bound for Fqlinear subsystem codes. It follows that no subsystem code over a prime field can beat the Singleton bound. On the other hand, we show the remarkable fact that there exist impure subsystem codes beating the Hamming bound. A number of open ...

Locally-correctable codes (LCCs) and locally-testable codes (LTCs) are codes that admit local algorithms for decoding and testing respectively. The local algorithms are randomized algorithms that make only a small number of queries to their input. LCCs and LTCs are both interesting in their own right, and have important applications in complexity theory. It is a well-known question what are the...

A central problem in coding theory is to determine Aq(n, 2e + 1), the maximal cardinality of a q-ary code of length n correcting up to e errors. When e is fixed and n is large, the best upper bound for A(n, 2e+1) (the binary case) is the well-known Johnson bound from 1962. This however simply reduces to the sphere-packing bound if a Steiner system S(e + 1, 2e + 1, n) exists. Despite the fact th...

We present some results that show that bounds from classical coding theory still work in many cases of quantum coding theory. 1 Nondegenerate Quantum Codes Let Q be an ((n,K, d)) nondegenerate quantum code with projection operator P . Let Ai and Bi be the quantum enumerators of Q, [1],[2] Ai = ∑ wt(E)=i Tr(EP )Tr(EP ), Bi = ∑ wt(E)=i Tr(EPEP ), where E is an error operator. (See [1],[2] for def...

In this paper we derive an upper bound for the average-case generalization error of the mixture of experts modular neural network, based on an average-case generalization error bound for an isolated neural network. By doing this we also generalize a previous bound for this architecture that was restricted to special problems. We also present a correction factor for the original average generali...

A new lower bound for the average probability or error for a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound has a structure very similar to the well-known sphere packing packing bound derived by Haroutunian. However, since explicitly imposes independence of the users’ input distributions (conditioned on the time-sharing auxiliary variable) results in a ti...

In this paper, we consider the adaptive Eulerian–Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a new a posteriori error bound for ELM semi-discretization. With the help of this proposed error bound, we are able to show the optimal convergence rate of ELM f...

of the bachelor's thesis Abstract: Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. A traditional approach is to look for codes which simultaneously maximize error tolerance and minimize storage space consumption. However, this tends to yield codes for which error correction requires an unrealistic amount of communication between storage nodes. LRCs s...

In this paper, network error control coding is studied for robust and efficient multicast in a directed acyclic network with imperfect links. The block network error control coding framework, BNEC, is presented and the capability of the scheme to correct a mixture of symbol errors and packet erasures and to detect symbol errors is studied. The idea of syndrome-based decoding and error detection...