New Lower Bounds on the Periodic Crosscorrelation of QAM Codes with Arbitrary Energy
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
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EURASIP Journal on Wireless Communications and Networking - Special issue on innovative signal transmission and detection techniques for next generation cellular CDMA systems
Periodic correlation bounds of binary sequence pairs
WiCOM'09 Proceedings of the 5th International Conference on Wireless communications, networking and mobile computing
Generalized bounds on partial aperiodic correlation of complex roots of unity sequences
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Lower Bounds on Correlation of Z-Complementary Code Sets
Wireless Personal Communications: An International Journal
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For the minimum aperiodic crosscorrelation θ(n,M) of binary codes of size M and length n over the alphabet {1,-1} there exists the celebrated Welch bound θ2(n,M)⩾(M-1)n2/2Mn-N-1 which was published in 1974 and remained in this form up to now. In the article this bound is strengthened for all M⩾4 and n⩾2. In particular, it is proved that θ2(n,M)⩾n-2n/√3M, M⩾3 and θ2(n,M)⩾n-[πn/√8M], M⩾5. In the asymptotic process when M tends to infinity as n→∞, these bounds are twice as large as the Welch bound and coincide with the corresponding asymptotic bound on the square of the minimum periodic crosscorrelation of binary codes. The main idea of the proof is a new sufficient condition for the mean value of a nonnegative definite matrix over the code to be greater than or equal to the average over the whole space. This allows one to take into account weights of cyclic shifts of code vectors and solve the problem of their optimal choice