On the binary weight distribution of some Reed-Solomon codes

Consider an (n,k) linear code with symbols from GF(2 sup M). If each code symbol is represented by a m-tuple over GF(2) using certain basis for GF(2 sup M), a binary (nm,km) linear code is obtained. The weight distribution of a binary linear code obtained in this manner is investigated. Weight enumerators for binary linear codes obtained from Reed-Solomon codes over GF(2 sup M) generated by polynomials, (X-alpha), (X-l)(X-alpha), (X-alpha)(X-alpha squared) and (X-l)(X-alpha)(X-alpha squared) and their extended codes are presented, where alpha is a primitive element of GF(2 sup M). Binary codes derived from Reed-Solomon codes are often used for correcting multiple bursts of errors

A concatenated coding scheme for error control

A concatenated coding scheme for error contol in data communications was analyzed. The inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if either the inner code decoder fails to make a successful decoding or the outer code decoder detects the presence of errors after the inner code decoding. Probability of undetected error of the proposed scheme is derived. An efficient method for computing this probability is presented. Throughout efficiency of the proposed error control scheme incorporated with a selective repeat ARQ retransmission strategy is analyzed

Coding for reliable satellite communications

Several error control coding techniques for reliable satellite communications were investigated to find algorithms for fast decoding of Reed-Solomon codes in terms of dual basis. The decoding of the (255,223) Reed-Solomon code, which is used as the outer code in the concatenated TDRSS decoder, was of particular concern

A concatenated coding scheme for error control

A concatenated coding scheme for error control in data communications is analyzed. The inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if the outer code detects the presence of errors after the inner code decoding. The probability of undetected error of the above error control scheme is derived and upper bounded. Two specific exmaples are analyzed. In the first example, the inner code is a distance-4 shortened Hamming code with generator polynomial (X+1)(X(6)+X+1) = X(7)+X(6)+X(2)+1 and the outer code is a distance-4 shortened Hamming code with generator polynomial (X+1)X(15+X(14)+X(13)+X(12)+X(4)+X(3)+X(2)+X+1) = X(16)+X(12)+X(5)+1 which is the X.25 standard for packet-switched data network. This example is proposed for error control on NASA telecommand links. In the second example, the inner code is the same as that in the first example but the outer code is a shortened Reed-Solomon code with symbols from GF(2(8)) and generator polynomial (X+1)(X+alpha) where alpha is a primitive element in GF(z(8))

Two hybrid ARQ error control schemes for near Earth satellite communications

Two hybrid Automatic Repeat Request (ARQ) error control schemes are proposed for NASA near Earth satellite communications. Both schemes are adaptive in nature, and employ cascaded codes to achieve both high reliability and throughput efficiency for high data rate file transfer

Extended Hubbard model on a C20_{20} molecule

The electronic correlations on a C$_{20}$ molecule, as described by an extended Hubbard Hamiltonian with a nearest neighbor Coulomb interaction of strength $V$, are studied using quantum Monte Carlo and exact diagonalization methods. For electron doped C$_{20}$, it is known that pair-binding arising from a purely electronic mechanism is absent within the standard Hubbard model (V=0). Here we show that this is also the case for hole doping for $0<U/t\leq 3$ and that, for both electron and hole doping, the effect of a non-zero $V$ is to work against pair-binding. We also study the magnetic properties of the neutral molecule, and find transitions between spin singlet and triplet ground states for either fixed $U$ or $V$ values. In addition, spin, charge and pairing correlation functions on C$_{20}$ are computed. The spin-spin and charge-charge correlations are very short-range, although a weak enhancement in the pairing correlation is observed for a distance equal to the molecular diameter.Comment: 9 pages, 8 figures, 4 table