Under random linear coding (RLC) scheme, we present a simple expression of the probability distribution p(D=K) for decoding delay D incurred by the lossy channel, where K is a positive integer. In contrast with the previous contribution, our focus is firstly on deriving the cumulative distribution function of the discrete random variable D over a perfect channel. One benefit of such dispose is that, from the overall viewpoint, computing the cumulative distribution function of delay D can be related with calculating the cardinalities of sets of some special matrices, so that the former can be obtained from the latter. Moreover, our expression of the probability distribution is an explicit form, and is valid for any number of packets M, freewill field size q and arbitrary channel loss rate ε.

In this letter, we present an improved method for the independence test procedure in the convolutional multicast algorithm proposed by Erez and Feder. We employ the linear independence test vectors to check the independence of the partial encoding vectors in the main program of Erez's convolutional multicast algorithm. It turns out that compared with the previous approach of computing the determinants of the correlative matrices, carrying out the independence test vectors can reduce the computational complexity.

In this letter, we first introduce a new generalized cyclotomic sequence of order two of length pq, then we calculate its linear complexity and minimal polynomial. Our results show that this sequence possesses both high linear complexity and optimal balance on 1 s and 0 s, which may be attractive for use in stream cipher cryptosystems.

Binary sequences with high linear complexity and high 2-adic complexity have important applications in communication and cryptography. In this paper, the 2-adic complexity of a class of balanced Whiteman generalized cyclotomic sequences which have high linear complexity is considered. Through calculating the determinant of the circulant matrix constructed by one of these sequences, the result shows that the 2-adic complexity of this class of sequences is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).

In this paper, we study Hermitian linear complementary dual (abbreviated Hermitian LCD) rank metric codes. A class of Hermitian LCD generalized Gabidulin codes are constructed by qm-self-dual bases of Fq2m over Fq2. Moreover, the exact number of qm-self-dual bases of Fq2m over Fq2 is derived. As a consequence, an upper bound and a lower bound of the number of the constructed Hermitian LCD generalized Gabidulin codes are determined.

In this paper, the correspondence between the weighted line graph and the Mason signal flow graph (MSFG) has been established, which gives an interpretation of a convolutional network code (CNC) over a cyclic network from a different perspective. Furthermore, by virtue of Mason theorem, we present two new equivalent conditions to evaluate whether the global encoding kernels (GEKs) can be uniquely determined by the given complete set of local encoding kernels (LEKs) in a CNC over a cyclic network. These two new equivalent conditions turn out to be more intuitive. Moreover, we give an alternative simple proof of an existing result.

In this paper, we further study linear network error correction code on a multicast network and attempt to establish a connection between linear network error correction codes and representable matroids. We propose a similar but more accurate definition of matroidal error correction network which has been introduced by K. Prasad et al. Moreover, we extend this concept to a more general situation when the given linear network error correction codes have different error correcting capacity at different sinks. More importantly, using a different method, we show that a multicast error correction network is scalar-linearly solvable if and only if it is a matroidal error correction network.

In this letter we propose a new Whiteman generalized cyclotomic sequence of order 4. Meanwhile, we determine its linear complexity and minimal polynomial. The results show that this sequence possesses both high linear complexity and optimal balance on 1 s and 0 s, which may be attractive for cryptographic applications.