We consider an energy harvesting transmitter sending status updates to a receiver over an erasure channel, where each status update is of length k symbols. The energy arrivals and the channel erasures are independent and identically distributed (i.i.d.) and Bernoulli distributed in each slot. In order to combat the effects of the erasures in the channel and the uncertainty in the energy arrival...

Quantum stabilizer states over Fm can be represented as self-dual additive codes over Fm2 . These codes can be represented as weighted graphs, and orbits of graphs under the generalized local complementation operation correspond to equivalence classes of codes. We have previously used this fact to classify self-dual additive codes over F4. In this paper we classify selfdual additive codes over ...

We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix. We show that the largest minimum distance can be achieved by a subcode of a Reed-Solomon code of small field size. As a by-product of this result, we settle the GM-MDS conjecture of Dau et. al. in the affirmative.

It is well known that erasure coding can be used in storage systems to efficiently store data while protecting against failures. Conventionally, the design of erasure codes has focused on the tradeoff between redundancy and reliability; under this criterion, an Maximum Distance Separable (MDS) code is optimal. However, practical storage systems call for additional considerations. In particular,...

The problem of determining Aq(n, d), the maximum cardinality of a q-ary code of length n with minimum distance at least d, is considered in some cases where corresponding MDS codes do not exist. Slight improvements of the Singleton bound are given, including Aq(q + 2, q) q3 − 3 if q is odd, A5(7, 5) 53 − 4 and A16(18, 15) 184 − 4. © 2004 Elsevier B.V. All rights reserved.

Disease Overview Ring sideroblasts (RS) are erythroid precursors with abnormal perinuclear mitochondrial iron accumulation. Two myeloid neoplasms defined by the presence of RS, include myelodysplastic syndromes RS (MDS-RS) and MDS/myeloproliferative neoplasm thrombocytosis (MDS/MPN-RS-T). Diagnosis MDS-RS is a lower risk MDS, single or multilineage dysplasia (MDS-RS-SLD/MLD), <5% bone marrow (B...

Maximum Distance Separable (MDS) codes are those error correction codes that meet the singleton bound, thus they have the largest minimum distance possible. The main research problem is to find an upper bound on the length of the codewords when the alphabet size and dimension of the code are fixed. This paper will present a new technique using the Partition Weight Enumerator for solving this pr...

The constraint complexity of a graphical realization of a linear code is the maximum dimension of the local constraint codes in the realization. The treewidth of a linear code is the least constraint complexity of any of its cycle-free graphical realizations. This notion provides a useful parametrization of the maximum-likelihood decoding complexity for linear codes. In this paper, we prove the...

In Reed-Solomon codes and all other maximum distance separable codes, there is an intrinsic relationship between the size of the symbols in a codeword and the length of the codeword. Increasing the number of symbols in a codeword to improve the efficiency of the coding system thus requires using a larger set of symbols. However, long Reed-Solomon codes are difficult to implement and many commun...