94 research outputs found
MWS and FWS Codes for Coordinate-Wise Weight Functions
A combinatorial problem concerning the maximum size of the (hamming) weight
set of an linear code was recently introduced. Codes attaining the
established upper bound are the Maximum Weight Spectrum (MWS) codes. Those
codes with the same weight set as are called Full
Weight Spectrum (FWS) codes. FWS codes are necessarily ``short", whereas MWS
codes are necessarily ``long". For fixed the values of for which
an -FWS code exists are completely determined, but the determination
of the minimum length of an -MWS code remains an open
problem. The current work broadens discussion first to general coordinate-wise
weight functions, and then specifically to the Lee weight and a Manhattan like
weight. In the general case we provide bounds on for which an FWS code
exists, and bounds on for which an MWS code exists. When specializing to
the Lee or to the Manhattan setting we are able to completely determine the
parameters of FWS codes. As with the Hamming case, we are able to provide an
upper bound on (the minimum length of Lee MWS codes),
and pose the determination of as an open problem. On the
other hand, with respect to the Manhattan weight we completely determine the
parameters of MWS codes.Comment: 17 page
A study of digital holographic filters generation. Phase 2: Digital data communication system, volume 1
An empirical study of the performance of the Viterbi decoders in bursty channels was carried out and an improved algebraic decoder for nonsystematic codes was developed. The hybrid algorithm was simulated for the (2,1), k = 7 code on a computer using 20 channels having various error statistics, ranging from pure random error to pure bursty channels. The hybrid system outperformed both the algebraic and the Viterbi decoders in every case, except the 1% random error channel where the Viterbi decoder had one bit less decoding error
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