Lower bounds on the minimum average distance of binary codes

Let β(n,M) denote the minimum average Hamming distance of a binary code of length n and cardinality M. In this paper we consider lower bounds on β(n,M). All the known lower bounds on β(n,M) are useful when M is at least of size about 2ⁿ⁻¹/n. We derive new lower bounds which give good estimations when size of M is about n. These bounds are obtained using a linear programming approach. In particular, it is proved that lim_n→∞β(n,2n)=5/2. We also give a new recursive inequality for β(n,M).     

广义Hamming重量的广义Griesmer界进一步分析

通过对q元线性码广义Hamming重量dr(·)的分析,应用支撑重量ωs(C)的性质,再次分析了q元[n,k]线性码广义Griesmer界n≥dr+sum from i=1 to k-r[(q-1)dr/qi(qr-1)].     

Hyperon beta-decay and axial charges of the lambda in view of strongly distorted baryon wave-functions

Within the collective coordinate approach to chiral soliton models we suggest that breaking of SU(3) flavor symmetry mainly resides in the baryon wave-functions while the charge operators maintain a symmetric structure. Sizable symmetry breaking in the wave-functions is required to reproduce the observed spacing in the spectrum of the  baryons. The matrix elements of the flavor symmetric charge operators nevertheless yield g_A/g_V ratios for hyperon beta-decay which agree with the empirical data approximately as well as the successful F&D parameterization of the Cabibbo scheme. Demanding the strangeness component in the nucleon to vanish in the two flavor limit of the model, determines the structure of the singlet axial charge operator and yields the various quark flavor components of the axial charge of the Λ-hyperon. The suggested picture gains support from calculations in a realistic model using pion and vector meson degrees of freedom to build up the soliton.     

Partial permutation decoding for the first-order Reed-Muller codes

Partial permutation decoding is shown to apply to the first-order Reed-Muller codes R(1,m), where m>4 by finding s-PD-sets for these codes for 2≤s≤4.     

Secure Polar Coding for the Primitive Relay Wiretap Channel

With the emergence of wireless networks, cooperation for secrecy is recognized as an attractive way to establish secure communications. Departing from cryptographic techniques, secrecy can be provided by exploiting the wireless channel characteristics; that is, some error-correcting codes besides reliability have been shown to achieve information-theoretic security. In this paper, we propose a polar-coding-based technique for the primitive relay wiretap channel and show that this technique is suitable to provide information-theoretic security. Specifically, we integrate at the relay an additional functionality, which allows it to smartly decide whether it will cooperate or not based on the decoding detector result. In the case of cooperation, the relay operates in a decode-and-forward mode and assists the communication by transmitting a complementary message to the destination in order to correctly decode the initial source’s message. Otherwise, the communication is completed with direct transmission from source to the destination. Finally, we first prove that the proposed encoding scheme achieves weak secrecy, then, in order to overcome the obstacle of misaligned bits, we implement a double-chaining construction, which achieves strong secrecy.     

The analysis of the error statistics in a 5 × 40 Gbit/s fibre link with hybrid amplification

We quantify the error statistics and patterning effects in a 5 × 40 Gbit/s WDM RZ-OOK SMF/DCF fibre link using hybrid Raman/EDFA amplification. By extensive use of a numerical model, we determine how the error statistics change with the transmission distance. This knowledge is used as a basis for a constrained coding technique in order to improve the transmission error rate. We propose an adaptive constrained code for mitigation of the patterning effects and demonstrate that this approach can substantially reduce the bit error rate (BER) even for very large values of the channel BER (BER > 10^− 1). The proposed technique can be used in combination with forward error correction schemes (FEC) to extend the range of channel BERs that an FEC scheme is effective over.     

Inhomogeneous Quantum Codes （III）： The Asymmetric Case

The stabilizer （additive） method and non-additive method for constructing asymmetric quantum codes have been established. In this paper, these methods are gen- eralized to inhomogeneous quantum codes.     

Overlap Cycles for Steiner Quadruple Systems

Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. It is well known that Steiner quadruple systems of order v, or SQS(v), exist if and only if . Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, are a type of cyclic Gray code. Overlap cycles are generalizations of universal cycles that were introduced in 2010 by Godbole, et al. Using Hanani's SQS constructions, we show that for every with there exists an SQS(v) that admits a 1‐overlap cycle.     

Minimal Symmetric Differences of Lines in Projective Planes

Let q be an odd prime power and let be the minimum size of the symmetric difference of r lines in the Desarguesian projective plane . We prove some results about the function , in particular showing that there exists a constant such that for .