2,316 research outputs found
Cyclic lowest density MDS array codes
Three new families of lowest density maximum-distance separable (MDS) array codes are constructed, which are cyclic or quasi-cyclic. In addition to their optimal redundancy (MDS) and optimal update complexity (lowest density), the symmetry offered by the new codes can be utilized for simplified implementation in storage applications. The proof of the code properties has an indirect structure: first MDS codes that are not cyclic are constructed, and then transformed to cyclic codes by a minimum-distance preserving transformation
On self-dual double circulant codes
Self-dual double circulant codes of odd dimension are shown to be dihedral in
even characteristic and consta-dihedral in odd characteristic. Exact counting
formulae are derived for them and used to show they contain families of codes
with relative distance satisfying a modified Gilbert-Varshamov bound.Comment: 8 page
Optimal Binary Locally Repairable Codes via Anticodes
This paper presents a construction for several families of optimal binary
locally repairable codes (LRCs) with small locality (2 and 3). This
construction is based on various anticodes. It provides binary LRCs which
attain the Cadambe-Mazumdar bound. Moreover, most of these codes are optimal
with respect to the Griesmer bound
New Classes of Partial Geometries and Their Associated LDPC Codes
The use of partial geometries to construct parity-check matrices for LDPC
codes has resulted in the design of successful codes with a probability of
error close to the Shannon capacity at bit error rates down to . Such
considerations have motivated this further investigation. A new and simple
construction of a type of partial geometries with quasi-cyclic structure is
given and their properties are investigated. The trapping sets of the partial
geometry codes were considered previously using the geometric aspects of the
underlying structure to derive information on the size of allowable trapping
sets. This topic is further considered here. Finally, there is a natural
relationship between partial geometries and strongly regular graphs. The
eigenvalues of the adjacency matrices of such graphs are well known and it is
of interest to determine if any of the Tanner graphs derived from the partial
geometries are good expanders for certain parameter sets, since it can be
argued that codes with good geometric and expansion properties might perform
well under message-passing decoding.Comment: 34 pages with single column, 6 figure
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