The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the co...The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors.Furthermore,the error correction capability and code rate tradeoff of these codes are also discussed.Thus,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.展开更多
Our studies about safety in society lead us to the most popular book by Karl Mannheim： Ideology and Utopia. This work envisages the discrepancies between social knowledge and the material world itself. The crucial co...Our studies about safety in society lead us to the most popular book by Karl Mannheim： Ideology and Utopia. This work envisages the discrepancies between social knowledge and the material world itself. The crucial conclusion reads as follows： Our image of reality is mostly based on our interests and desires and does not rely on thorough research. There are two types of such representations： utopia and ideology. The first of them, less interesting for us, is the type of ideas which can revolutionize a social being. The second one is a particular set of visions which can never be realized but on the other hand they act as common knowledge （general knowledge of the world）--stabilizing the social structure by presenting it with a holistic image of the world. Taking the above into consideration, how is it possible that representations, being so distant from reality （creating a completely separate ＂world＂）, basically enable efficient functioning in it？ Ideology, being the foundation of the society＇s functioning space, should always be tautological, in the sense that for the participants of the given world＇s image （creation as it is）, it should define the being in a comprehensive and adequate way （in Thomas Aquinas spirit）. What is more, it would always be true. We should also mention that the main tools of ideology, understood this way, are specific definitions and the extrapolation of sense. The purpose of this lecture is to prove that it is possible for ideology to come to life, only when the individuals who acknowledge it will consider their image of reality proper. The above ideological system should be understood as the obviousness of description of the surrounding world which in return makes unreflective functioning in reality possible. This obviousness of the presented world will be referred to as social safety.展开更多
基金The authors extend their gratitude to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under grant number R.G.P.1/85/42.
文摘The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors.Furthermore,the error correction capability and code rate tradeoff of these codes are also discussed.Thus,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.
文摘Our studies about safety in society lead us to the most popular book by Karl Mannheim： Ideology and Utopia. This work envisages the discrepancies between social knowledge and the material world itself. The crucial conclusion reads as follows： Our image of reality is mostly based on our interests and desires and does not rely on thorough research. There are two types of such representations： utopia and ideology. The first of them, less interesting for us, is the type of ideas which can revolutionize a social being. The second one is a particular set of visions which can never be realized but on the other hand they act as common knowledge （general knowledge of the world）--stabilizing the social structure by presenting it with a holistic image of the world. Taking the above into consideration, how is it possible that representations, being so distant from reality （creating a completely separate ＂world＂）, basically enable efficient functioning in it？ Ideology, being the foundation of the society＇s functioning space, should always be tautological, in the sense that for the participants of the given world＇s image （creation as it is）, it should define the being in a comprehensive and adequate way （in Thomas Aquinas spirit）. What is more, it would always be true. We should also mention that the main tools of ideology, understood this way, are specific definitions and the extrapolation of sense. The purpose of this lecture is to prove that it is possible for ideology to come to life, only when the individuals who acknowledge it will consider their image of reality proper. The above ideological system should be understood as the obviousness of description of the surrounding world which in return makes unreflective functioning in reality possible. This obviousness of the presented world will be referred to as social safety.
