Notes on two constructions of zero-difference balanced (ZDB) functions are made in this letter. Then ZDB functions over Ze×∏ki=0 Fqi are obtained. And it shows that all the known ZDB functions using cyclotomic cosets over Zn are special cases of a generic construction. Moreover, applications of these ZDB functions are presented.

Constant weight codes have mathematical interest and practical applications such as coding for bandwidth-efficient channels and construction of spherical codes for modulation. In this letter, by using difference balanced functions with d-form property, we constructed a class of constant composition code with new parameters, which achieves the equal sign of generalized Johnson bound.

Based on cyclic difference sets, sequences with two-valued autocorrelation can be constructed. Using these constructed sequences, two classes of binary constant weight codes are presented. Some codes proposed in this paper are proven to be optimal.

Let A(n, d, w) denote the maximum possible number of code words in binary (n,d,w) constant weight codes. For smaller instances of (n, d, w)s, many improvements have occurred over the decades. However, unknown instances still remain for larger (n, d, w)s (for example, those of n > 30 and d > 10). In this paper, we propose a new class of binary constant weight codes that fill in the remaining blank instances of (n, d, w)s. Specifically, we establish several new non-trivial lower bounds such as 336 for A(64, 12, 8), etc. (listed in Table 2). To obtain these results, we have developed a new systematic technique for construction by means of groups acting on some sets. The new technique is performed by considering a triad (G, Ω, f) := ("Group G," "Set Ω," "Action f on Ω") simultaneously. Our results described in Sect. 3 are obtained by using permutations of the elements of a set that include ∞ homogeneously like the other elements, which play a role to improve their randomness. Specifically, in our examples, we adopt the following model such as (PGL2(Fq), P1(Fq), "linear fractional action of subgroups of PGL2(Fq) on P1(Fq)") as a typical construction model. Moreover, as an application, the essential examples in [7] constructed by using an alternating group are again reconstructed with our new technique of a triad model, after which they are all systematically understood in the context of finite subgroups that act fractionally on a projective space over a finite field.

In the letter, properties of m-sequence are derived, based on these properties, a family of binary nonlinear constant weight codes is presented, these binary nonlinear constant weight codes can apply to automatic repeat request (ARQ) communication system, as detecting-error codes.

The bandwidth occupied by individual telecommunication devices in the field of mobile radio communication must be narrow in order to effectively exploit the limited frequency band. Therefore, it is necessary to implement low-bit-rate speech coding that is robust against background noise. We examine vector quantization using a neural network (NNVQ) as a robust LSP encoder. In this paper, we compare four types of binary patterns of a hidden layer, and clarify the dependency of quantization distortion on the bit pattern. By delayed decision (selection of low-distortion codes in decoding, i.e., EbD method) the spectral distortion (SD) can be decreased by 0.8 dB (20%). For noisy speech, the performance of the EbD method is better than that of the conventional VQ codebook mapping method. In addition, the SD can be decreased by 2.3 dB (40%) by using a method in which the neural networks for encoding and decoding are combined and re-trained. Finally, we examine the SD for speech having different signal-to-noise ratios (SNRs) from that used in training. The experimental results show that training using SNR between 30 and 40 dB is appropriate.

In this paper, a new encoding/decoding scheme of multiple-valued separable balanced codes is presented. These codes have 2m information digits and m (R - 2) check digits in radices R 4, 2m - 1 information digits and m + 1 check digits in R = 3, where code-length n = Rm. In actual use of code-lengths and radices, it is shown that the presented codes are relatively efficient in comparison with multiple-valued Berger codes which are known as optimal unordered codes. Meanwhile, the optimality of multiple-valued Berger codes is discussed.

The paper considers the design of two families of binary block codes developed for controlling large numbers of errors which may occur in LSI, optical disks and other devices. The semidistance codes are capable of assuring a required signal-to-noise ratio in information retrieval; the t-symmetric error correcting/all unidirectional error detecting" (t-SyEC/AUED) codes are capable of correcting t or fewer symmetric errors and also detecting any number of unidirectional errors caused by the asymmetric nature of transmission or storage madia. The paper establishes an equivalence between these families of codes, and proposes improved methods for constructing, for any values of t, a class of nonsystematic constant weight codes as well as a class of systematic codes. The constructed codes of both classes are shown to be optimal when t is O, and of asymptotically optimal order" in general cases. The number of redundant bits of the obtained nonsystematic code is of the order of (t+1/2)log2 K bits, where K is the amount of information encoded. The obtained systematic codes have redundancy of the order of (t+1)log2 K bits.

This letter considers a subclass of t-symmetric error correcting/all unidirectional error detecting (t-SyEC/AUED) codes in which the information is represented in an m-out-of-k coded form, which thus can be regarded as virtually systematic for practical purposes. For t3, previous researchers proposed methods for constructing codes of this subclass which are either optimal or of asymptotically optimal order. This letter proposes a new method for constructing, for any values of t, m and k, codes that are either optimal or of asymptotically optimal order. The redundancy of the obtained code is of the order tlog2k bits when mt.