On ℤ2ℤ2[u]-additive codes

In this paper, a new class of additive codes which is referred to as ?₂ ?₂[u]-additive codes is introduced. This is a generalization towards another direction of recently introduced ?₂ ?₄-additive codes [J. Borges, C. Fernández-Córdoba, J. Pujol, J. Rif´a, and M. Villanueva, ?₂ ?₄-linear codes: Generator matrices and duality, Designs Codes Cryptogr. 54(2) (2010), pp. 167–179]. ?₂ ?₄-additive codes have shown to provide a promising class of codes with their algebraic structure and applications such as steganography. The standard generator matrices are established and by introducing orthogonality the parity-check matrices are also obtained. A MacWilliams-type identity that relates the weight enumerator of a code with its dual is proved. Furthermore, a Gray map that maps these codes to binary codes is defined and some examples of optimal codes which are the binary Gray images of ?₂ ?₂[u]-additive codes are presented.     

On the generators of /spl Zopf//sub 4/ cyclic codes of length 2/sup e/

Results are presented on the generators of ideals in the ring /spl Zopf//sub 4/[x]/(x/sup n/-1). In particular, each ideal (cyclic code) has a unique distinguished set of generators that characterizes any cyclic code. Some results about dual codes are also included.     

Asymptotic performance comparison of concatenated (turbo) codes over GF(4)

In this paper, we investigate and compare the asymptotic performance of concatenated convolutional coding schemes over GF(4) over additive white Gaussian noise (AWGN) channels. Both parallel concatenated codes (PCC) and serial concatenated codes (SCC) are considered. We construct such codes using optimal non‐binary convolutional codes where optimality is in the sense of achieving the largest minimum distance for a fixed number of encoder states. Code rates of the form k₀/(k₀ + 1) for k₀=1, 8, and 64 are considered, which suite a wide spectrum of communications applications. For all of these code rates, we find the minimum distance and the corresponding multiplicity for both concatenated code systems. This is accomplished by feeding the encoder with all possible weight‐two and weight‐three input information patterns and monitoring, at the output of the encoder, the weight of the corresponding codewords and their multiplicity. Our analytical results indicate that the SCC codes considerably outperform their counterpart PCC codes at a much lower complexity. Inspired by the superiority of SCC codes, we also discuss a mathematical approach for analysing such codes, leading to a more comprehensive analysis and allowing for further improvement in performance by giving insights on designing a proper interleaver that is capable of eliminating the dominant error patterns. Copyright © 2004 John Wiley & Sons, Ltd.     

Wavelets approach for optimal boundary control of cellular uptake in tissue engineering

The control of the uptake of growth factors in tissue engineering is mathematically modelled by a partial differential equation subject to boundary and initial conditions. The main objective is to regulate cellular processes for the growth or regeneration of a tissue within an assigned terminal time. The techniques of basis function expansion and direct state parameterization were employed to yield efficient computational methods for this problem. Using Legendre and Chebyshev wavelets, the optimal control of the lumped-parameter system was transformed into a system of algebraic equations. The computational efficiency and effectiveness of the proposed method are illustrated by numerical examples.