Let m, k be positive integers with m=2k and k≥3. Let C(u, ν) is a class of cyclic codes of length 2m-1 whose parity-check polynomial is mu(x)mν(x), where mu(x) and mν(x) are the minimal polynomials of α-u and α-ν over GF(2). For the case $(u, u)=(1,rac{1}{3}(2^m-1))$, the weight distributions of binary cyclic codes C(u, ν) was determined in 2017. This paper determines the weight distributions of the binary cyclic codes C(u, ν) for the case of (u, ν)=(3, 2k-1+1). The application of these cyclic codes in secret sharing is also considered.

The purpose of document modeling is to learn low-dimensional semantic representations of text accurately for Natural Language Processing tasks. In this paper, proposed is a novel attention-based hybrid neural network model, which would extract semantic features of text hierarchically. Concretely, our model adopts a bidirectional LSTM module with word-level attention to extract semantic information for each sentence in text and subsequently learns high level features via a dynamic convolution neural network module. Experimental results demonstrate that our proposed approach is effective and achieve better performance than conventional methods.

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let C(t,e) denote the cyclic code with two nonzero αt and αe, where α is a generator of 𝔽*3m. In this letter, we investigate the ternary cyclic codes with parameters [3m - 1, 3m - 1 - 2m, 4] based on some results proposed by Ding and Helleseth in 2013. Two new classes of optimal ternary cyclic codes C(t,e) are presented by choosing the proper t and e and determining the solutions of certain equations over 𝔽3m.