129 research outputs found
The coset weight distributions of certain BCH codes and a family of curves
We study the distribution of the number of rational points in a family of
curves over a finite field of characteristic 2. This distribution determines
the coset weight distribution of a certain BCH code.Comment: Plain Tex, 15 pages; some numerical data adde
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
On the Peak-to-Mean Envelope Power Ratio of Phase-Shifted Binary Codes
The peak-to-mean envelope power ratio (PMEPR) of a code employed in
orthogonal frequency-division multiplexing (OFDM) systems can be reduced by
permuting its coordinates and by rotating each coordinate by a fixed phase
shift. Motivated by some previous designs of phase shifts using suboptimal
methods, the following question is considered in this paper. For a given binary
code, how much PMEPR reduction can be achieved when the phase shifts are taken
from a 2^h-ary phase-shift keying (2^h-PSK) constellation? A lower bound on the
achievable PMEPR is established, which is related to the covering radius of the
binary code. Generally speaking, the achievable region of the PMEPR shrinks as
the covering radius of the binary code decreases. The bound is then applied to
some well understood codes, including nonredundant BPSK signaling, BCH codes
and their duals, Reed-Muller codes, and convolutional codes. It is demonstrated
that most (presumably not optimal) phase-shift designs from the literature
attain or approach our bound.Comment: minor revisions, accepted for IEEE Trans. Commun
Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications
Coding; Communications; Engineering; Networks; Information Theory; Algorithm
Efficient fault-tolerant quantum computing
Fault tolerant quantum computing methods which work with efficient quantum
error correcting codes are discussed. Several new techniques are introduced to
restrict accumulation of errors before or during the recovery. Classes of
eligible quantum codes are obtained, and good candidates exhibited. This
permits a new analysis of the permissible error rates and minimum overheads for
robust quantum computing. It is found that, under the standard noise model of
ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an
order of magnitude larger than the logical machine contained within it in order
to be reliable. For example, a scale-up by a factor of 22, with gate error rate
of order , is sufficient to permit large quantum algorithms such as
factorization of thousand-digit numbers.Comment: 21 pages plus 5 figures. Replaced with figures in new format to avoid
problem
- …