We propose a construction of rate-compatible punctured codes based on protographs that have a special ERC structure in their parity part (ERC codes were introduced in Kim, Ramamoorthy and McLaughlin ‘06) . The protograph representation of these codes facilitates their asymptotic performance analysis and allows the implementation of high speed decoders. The construction process starts with a goo...

We show for binary Armstrong codes Arm(2, k, n) that asymptotically n/k ≤ 1.224, while such a code is shown to exist whenever n/k ≤ 1.12. We also construct an Arm(2, n− 2, n) and Arm(2, n− 3, n) for all admissible n.

We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between selforthogonal codes over F4 and binary quantum codes to one between selforthogonal codes over Fq2 and q-ary quantum codes for any prime power q. Index Terms — quantum stabilizer codes, nonbinary quantum codes, selforthogonal codes.

A class of rate-one space-time block codes (STBC) allowing the decoding of transmitted symbols into four groups is recently proposed by Yuen, Guan and Tjhung. This code is called four-group decodable STBC (4Gp-STBC). In this paper, the equivalent channel of 4Gp-STBC is derived and a new method to decode 4Gp-STBC based on sphere decoders is proposed. Furthermore, the performance of 4Gp-STBC is a...

Consider representation theory associated to symmetric groups, or to Hecke algebras in type A, or to q-Schur algebras, or to finite general linear groups in non-describing characteristic. Rock blocks are certain combinatorially defined blocks appearing in such a representation theory, first observed by R. Rouquier. Rock blocks are much more symmetric than general blocks, and every block is deri...

Balanced incomplete-block designs (BIBDs) with repeated blocks are studied and constructed. We continue work initiated by van Lint and Ryser in 1972 and pursued by van Lint in 1973. We concentrate on constructing (v, b, r, k, λ)-BIBDs with repeated blocks, especially those with gcd(b, r, λ) = 1 and r ≤ 20. We obtain new bounds for the multiplicity of a block in terms of the parameters of a BIBD...

Identifying and locating-dominating codes have been studied widely in circulant graphs of type Cn(1, 2, 3, . . . , r) over the recent years. In 2013, Ghebleh and Niepel studied locatingdominating and identifying codes in the circulant graphs Cn(1, d) for d = 3 and proposed as an open question the case of d > 3. In this paper we study identifying, locating-dominating and self-identifying codes i...

We define the concepts of an injective colouring and the injective chromatic number of a graph and give some upper and lower bounds in general, plus some exact values. We explore in particular the injective chromatic number of the hypercube and put it in the context of previous work on similar concepts, especially the theory of errorcorrecting codes. Finally, we give necessary and sufficient co...