One of the fundamental problems in coding theory is to determine, for given set of parameters q, n and d, the value Aq(n,d), which is the maximum possible number of code words in a q-ary code of length n and minimum distance d. Codes that attain the maximum are said to be optimal. Being unknown for certain set of parameters, scientists have determined lower bounds, and researchers investigated ...

The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that are capable of implementing a universal set of gates with error rates below approximately 1%, requirements compatible with experimental reality. Consequentl...

We investigate the construction of prefix-free and fix-free codes with specified codeword compositions. We present a polynomial time algorithm which constructs a fix-free code with the same codeword compositions as a given code for a special class of codes called distinct codes. We consider the construction of optimal fix-free codes which minimize the average codeword cost for general letter co...

For a systematic erasure code, update complexity (UC) is defined as the maximum number of parity blocks needed to be changed when some information blocks are updated. Locally repairable codes (LRCs) have been recently proposed and used in real-world distributed storage systems. In this paper, update complexity of optimal LRCs is studied and both lower and upper bounds on UC are established in t...

Low encoding/decoding complexity is essential for practical RAID-6 storage systems. In this paper, we describe a new coding scheme, which we call Rotary-code, for RAID-6 disk arrays. We construct Rotarycode based on a bit matrix-vector product similar to the Reed-Solomon coding, and provide the geometry encoding method and detailed non-recursive decoding algorithms. The capability of two-disk f...

The objective of this work is to design optimal codes for a 2 Dimensional Optical Code Division Multiple Access system (2D-OCDMA), and to test their robustness to noise perturbation. 2D coding is performed by Multi-Wavelength Optical Orthogonal Codes (MWOOC). They are obtained with our new construction method which permits to choose the code parameters with high flexibility. Different receiver ...

We consider the problem of finding a trellis for a finear block code that minimizes one or more measures of trellis complexity. The domain of optimization may be different permutations of the same code or different codes with the same parameters. Constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code, are used to derive bounds on comple...