11507660
Existence of perfect Mendelsohn designs with k=5 and lambda>1
Abstract Let υ, k , and λ be positive integers. A (υ, k , λ )- Mendelsohn design (briefly (υ, k , λ )-MD) is a pair ( X , B ) where X is a υ-set (of points ) and B is a collection of cyclically ordered k -subsets of X (called blocks ) such that every ordered pair of points of X are consecutive in exactly λ blocks of B . A set of k distinct elements { a 1 , a 2 ,…, a k } is said to be cyclically ordered by a 1 a 2 a k a 1 and the pair a i , a i + t is said to be t -apart in cyclic k -tuple ( a 1 , a 2 ,…, a k ) where i + t is taken modulo k . It for all t =1,2,…, k -1, every ordered pair of points of X is t -apart in exactly λ blocks of B , then the (υ, k , λ )-MD is called a perfect design and is denoted briefly by (υ, k , λ )-PMD. In this paper, we shall be concerned mainly with the case where k =5 and λ >1. It will be shown that the necessary condition for the existence of a (υ, 5, λ )-PMD, namely, λv ( υ -1)≡0 (mod 5), is also sufficient for λ >1 with the possible exception of pairs (υ, λ ) where λ =5 and υ =18 and 28.
22049562
Existence of holey 3-GDDs of type (u, gtw1)
Abstract In this paper, the necessary and sufficient conditions for the existence of a group divisible design with block size three, u groups, t holes of size ug and one hole of size uw are given.
5254546
Constructions for Perfect 5-Deletion-Correcting Codes of Length$7$
There are two kinds of perfect (k-t)-deletion-correcting codes with words of length k over an alphabet of size v, those where the coordinates may be equal and those where all coordinates must be different. We call these two kinds of codes T*(t,k,v)-codes and T(t,k,v)-codes respectively. Both a T*(t,k,v)-code and a T(t,k,v)-code are capable of correcting any combination of up to (k-t) deletions and insertions of letters occurred in transmission of codewords. In this correspondence, we consider constructions for the codes from directed designs. By means of these constructions, the existence of a T(2,7,v)-code is settled for all positive integers v with the exception of 68 values of v; T*(2,7,v)-codes are constructed for all integers vges2350. A large number of explicit constructions for T*(2,7,v)-codes with v<2350 are also presented
14835961
North-Holland On the existence of perfect Mendelsohn designs with k = 7 and A even
Let v, k and I be positive integers. A (v, k, A)-Mendelsohn design (briefly (v, k, A)-MD) is a pair (X, 3) where X is a v-set (of points) and !?8 is a collection of cyclically ordered k-subsets of X (called blocks) such that every ordered pair of points of X are consecutive in exactly il blocks of 3. A set of k distinct elements {a,, a-,, . . . , ak} is said to be cyclically ordered by a,Ca,C.‘<a&a, and the pair a,, a,,, are said to be t-apart in a cyclic k-tuple (a,, az, . . . , ak) where i + I is taken modulo k. If for all t = 1, 2, . . . , k 1, every ordered pair of points of X are t-apart in exactly )L blocks of 3, then the (v, k, A)-MD is called perfect and is denoted briefly by (v, k, A)-PMD. A necessary condition for the existence of a (v, k, A)-PMD is Av(v 1) = 0 (mod k). In this paper, we shall be concerned mostly with the case k = 7 and il even. It will be shown ttat the necessary condition for the existence of a (v, 7, A)-PMD, namely Av(v 1) = 0 (mod 7), is also sufficient for all even A 2 16, with at most 29 possible exceptions for the pair (v, A) where A is even and E. < 16. In the process, we shall also establish that the necessary condition v = 0 or 1 (mod 7) for the existence of a (v, 7, I)-PMD is also sufficient for all v 2 421 with at most 40 possible exceptions below this value, which improves the earlier results.
29194002
On the existence of perfect Mendelsohn designs with k = 7 and lambda even
Abstract Let v, k and λ be positive integers. A ( v, k , λ)- Mendelsohn design (briefly ( v, k , λ)-MD) is a pair ( X ,B) where X is a v -set (of points ) andBis a collection of cyclically ordered k -subsets of X (called blocks ) such that every ordered pair of points of X are consecutive in exactly λ blocks of B. A set of k distinct elements { a 1 , a 2 , ..., a k } is said to be cyclically ordered by a 1 a 2 a k a 1 and the pair a i , a i + t are said to be t -part in a cyclic k -tuple ( a 1 , a 2 ,..., a k ) where i + t is taken modulo k . If for all t = 1, 2,..., k − 1, every ordered pair of points of X are t -apart in exactly λ blocks of B, then the ( v, k , λ)-MD is called perfect and is denoted briefly by ( v, k , λ)-PMD. A necessary condition for the existence of a ( v, k , λ)-PMD is λ v ( v −1)≡0 (mod k ). In this paper, we shall be concerned mostly with the case k = 7 and λ even. It will be shown that the necessary condition for the existence of a v , 7, λ)-PMD, namely λ v ( v −1)≡0 (mod 7), is also sufficient for all even λ ⪖ 16, with at most 29 possible exceptions for the pair ( v , λ) where λ is even and λ v ≡0 or 1 (mod 7) for the existence of a ( v , 7, 1)-PMD is also sufficient for all v ⪖ 421 with at most 40 possible exceptions below this value, which improves the earlier results.
18873920
Signal Sets From Functions With Optimum Nonlinearity
Signal sets with the best correlation property are desirable in code-division multiple-access (CDMA) systems. In this paper, the construction of Wootters and Fields for mutually unbiased bases is extended into a generic construction of signal sets using planar functions. Then, specific classes of planar functions and almost bent functions are employed to obtain (q2+q,q) signal sets. The signal sets derived from planar functions are optimal with respect to the Levenstein bound, and those obtained from almost bent functions nearly meet the Levenstein bound. The signal sets constructed in this paper could have a very small alphabet size, and have applications in synchronous DS-CDMA systems, where the number of users is greater than the signal space dimension or the spreading factor
18219094
Nonuniform sequential sampling for signal analysis
New electronic technologies for signal analysis raise the possibility of sampling very rapidly, with a time-varying density, and determining empirically both the sampling rate and the window width as the signal evolves in time. These opportunities also point to the possibility of sequentially sampling in a time-varying way in more traditional problems. Motivated by these ideas, we establish a sampling formula, valid in cases where both sampling rate and window width may be varied. The formula states that, in terms of the ways in which these quantities should alter with time, optimal performance is achieved when the window width is inversely proportional to squared sampling rate, and sampling rate is directly proportional to squared bias.
16485753
An integrated approach to robust speaker identification and speech recognition
Conventional speaker identification and speech recognition algorithms cannot deal with noisy and multiple speaker environments. For example, IBM via Voice has low recognition rates if dictation is done in a noisy environment. In order to achieve high performance in speaker identification and speech recognition, we propose an integrated approach that takes every facet of the process into account. Here we summarize some preliminary results from the application of this integrated approach to robust speaker identification and speech recognition. A real-time stand-alone software prototype has been developed to evaluate the effectiveness of the approach.
123278
Enhanced speech in noisy multiple speaker environment
Noisy environments seriously degrade the performance of speech recognition systems. Here we implement a high performance speech enhancement algorithm. Data from speech separation challenge were used to evaluate the method. It was observed that the enhanced speech significantly improved the recognition performance. In 2 out of 4 SNR cases, over 100% relative percentage improvements were achieved. Standalone software prototype has been developed and evaluated.
7184753
Speech separation algorithms for multiple speaker environments
Conventional speaker identification and speech recognition algorithms do not perform well if there are multiple speakers in the background. For high performance speaker identification and speech recognition applications in multiple speaker environments, a speech separation stage is essential. Here we summarize the implementation of three speech separation techniques. Advantages and disadvantages of each method are highlighted, as no single method can work under all situations. Stand-alone software prototypes for these methods have been developed and evaluated.
109716942
A nanoscale nonvolatile memory device made from RbAg4I5 solid electrolyte grown on a Si substrate
A nanoscale nonvolatile memory device made from RbAg"4I"5 solid electrolyte has been made directly on a Si substrate with lateral size scaled down to 100nm. By applying voltages with different polarity, the device could be switched between high- and low-resistance states. The ratio between the high and low resistances could reach ~10^3, and the low-resistance state showed rectifying diode characteristics. The configured resistances remained nonvolatile after switching, and the device could be switched repeatedly for ~10^3 times. Our results show that the nanoscale nonvolatile memory device can be integrated directly with Si-based circuit and can be potentially used for high-density memory application.