Generalized and Extended Product Codes

Inferences for Extended Generalized Exponential Distribution based on Order Statistics

‎Recently‎, ‎a new distribution‎, ‎named as extended generalized exponential distribution‎, ‎has been introduced by Kundu and Gupta (2011). ‎In this paper‎, ‎we consider the extended generalized exponential distribution with known shape parameters α and β. ‎At first‎, ‎the exact expressions for marginal and product moments of o...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

Generalized Extended Hamming Codes over Galois Ring of Characteristic $2^{n}$

In this paper, we introduce generalized extended Hamming codes over Galois rings GR(2,m) of characteristic 2 with extension degree m. Furthermore we prove that the minimum Hamming weight of generalized extended Hamming codes over GR(2,m) is 4 and the minimum Lee weight of generalized extended Hamming codes over GR(8,m) is 6 for all m ≥ 3. ——————————————————————– ———Received May 25, 2011. This w...

Quantum Codes from Generalized Reed-Solomon Codes and Matrix-Product Codes

One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized Reed-Solomon codes. We also present some classes of quantum codes from matrix-product codes. It turns out that many of our quantum codes are new in the sense that the ...

A general construction of Reed-Solomon codes based on generalized discrete Fourier transform

In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes  enjoy nice algebraic properties just as the classic one.