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161.
Self-dual codes over exist for all even lengths. The smallest length for which the largest minimum weight among self-dual codes has not been determined
is 24, and the largest minimum weight is either 9 or 10. In this note, we show that there exists no self-dual [24, 12, 10]
code over , using the classification of 24-dimensional odd unimodular lattices due to Borcherds.
相似文献
162.
Elena Cordero Karlheinz Grö chenig 《Proceedings of the American Mathematical Society》2005,133(12):3573-3579
We study time-frequency localization operators of the form , where is the symbol of the operator and are the analysis and synthesis windows, respectively. It is shown in an earlier paper by the authors that a sufficient condition for , the Schatten class of order , is that belongs to the modulation space and the window functions to the modulation space . Here we prove a partial converse: if for every pair of window functions with a uniform norm estimate, then the corresponding symbol must belong to the modulation space . In this sense, modulation spaces are optimal for the study of localization operators. The main ingredients in our proofs are frame theory and Gabor frames. For and , we recapture earlier results, which were obtained by different methods.
163.
Hai Huyen Dam Hans-Jürgen Zepernick Sven Nordholm Jörgen Nordberg 《Annals of Operations Research》2005,133(1-4):249-264
The performance of a code division multiple access system depends on the correlation properties of the employed spreading
code. Low cross-correlation values between spreading sequences are desired to suppress multiple access interference and to
improve bit error performance. An auto-correlation function with a distinct peak enables proper synchronization and suppresses
intersymbol interference. However, these requirements contradict each other and a trade-off needs to be established. In this
paper, a global two dimensional optimization method is proposed to minimize the out-of-phase average mean-square aperiodic
auto-correlation with average mean-square aperiodic cross-correlation being allowed to lie within a fixed region. This approach
is applied to design sets of complex spreading sequences. A design example is presented to illustrate the relation between
various correlation characteristics. The correlations of the obtained sets are compared with correlations of other known sequences. 相似文献
164.
整表代数是群代数的推广,它的理想是群代数码的推广.本文给出了整表代数的单边理想是自正交理想的必要充分条件. 相似文献
165.
In this paper, codes over F5 with parameters [36, 18, 12], [48, 24, 15], [60, 30, 18], [64, 32, 18] and [76, 38, 21] which improve the previously known bounds on the minimum weight for linear codes over F5 are constructed from conference matrices. Through shortening and truncating, the above codes give numerous new codes over F5 which improve the previously known bounds on minimum weights. 相似文献
166.
Hans Georg Schaathun 《Designs, Codes and Cryptography》2004,31(1):27-42
A greedy 1-subcode is a one-dimensional subcode of minimum (support) weight. A greedy r-subcode is an r-dimensional subcode with minimum support weight under the constraint that it contain a greedy (r - 1)-subcode. The r-th greedy weight e
r is the support weight of a greedy r-subcode. The greedy weights are related to the weight hierarchy. We use recent results on the weight hierarchy of product codes to develop a lower bound on the greedy weights of product codes. 相似文献
167.
Bora Moon 《Discrete Mathematics》2018,341(11):3174-3181
It is known that the binary generalized Goppa codes are perfect codes for the weighted Hamming metrics. In this paper, we present the existence of a weighted Hamming metric that admits a binary Hamming code (resp. an extended binary Hamming code) to be perfect code. For a special weighted Hamming metric, we also give some structures of a 2-perfect code, show how to construct a 2-perfect linear code and obtain the weight distribution of a 2-perfect code from the partial information of the code. 相似文献
168.
169.
In this paper, we use character-theoretic techniques to give new nonexistence results for -strong external difference families (SEDFs). We also use cyclotomic classes to give two new classes of SEDFs with . 相似文献
170.