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In this paper, we extend two earlier works further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions. It is interesting to note that many cyclic codes in the family are optimal and have only a few non-zero weights. Besides using similar ideas, we carry out some subtle manipulation of certain exponential sums.
We give an example of a non-commutative mono-tone polynomial f which can be computed by a polynomial-size non-commutative formula, but every monotone non-commutative circuit computing f must have an exponential size. In the non-commutative setting this gives, a fortiori, an exponential separation between monotone and general formulas, monotone and general branching programs, and monotone and general...
The algorithm presented in [21] provides a method for the computation of the general solution of a polynomial matrix Diophantine equation. In this work we extend this algorithm for the n-D PMDE. We present a method to efficiently address the division of multivariate polynomials. The theory is implemented via illustrative examples.
Hybrid systems are a clean modeling framework for embedded systems, which feature integrated discrete and continuous dynamics. A well-known source of complexity comes from the time invariants, which represent an implicit quantification of a constraint over all time points of a continuous transition. Emerging techniques based on Satisfiability Modulo Theory (SMT) have been found promising for the verification...
Wireless sensor networks consist of a large number sensors spread across a given geographical area. Each sensor has its own communication capability as well as certain level of intelligence for signal processing and networking. As the sensor nodes are densely populated, communication range requirement for these nodes is smaller. After signal detection, a number of sensor nodes communicate over the...
Correlative minimum shift keying (MSK), a second order polynomial modulation scheme known as tamed frequency modulation (TFM), is a constant envelope type of modulation with a perfect peak to average power ratio (PAPR), besides the property of low out of band power. We apply the linearized TFM to the single carrier transmission with frequency domain equalization (SC/FDE) concept. We then obtain a...
Unequal error protection is the key to future transport of multimedia data. The paper presents an overview of some new approaches realizing UEP properties in physical transport, especially multicarrier modulation, or with LDPC and turbo codes. For multicarrier modulation, a UEP bit-loading method is described allowing for an arbitrary number of classes, arbitrary SNR margins between the classes and...
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