Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic. In this paper, based on the augmentation technique, we present two families of linear codes from some functions over finite fields. The first family of linear codes is constructed from monomial functions over finite fields. The weight distribution of the codes is determined in some cases. The codes are proved to be both optimally or almost optimally extendable and self-orthogonal under certain conditions. The localities of the codes and their duals are also studied and we obtain an infinite family of optimal or almost optimal locally recoverable codes. The second family of linear codes is constructed from weakly regular bent functions over finite fields and its weight distribution is explicitly determined. This family of codes is also proved to be both optimally or almost optimally extendable and self-orthogonal. Besides, this family of codes has been proven to have locality 2 or 3 under certain conditions. Particularly, we derive two infinite families of optimal locally recoverable codes. Some infinite families of 2-designs are obtained from the codes in this paper as byproducts.

The self-orthogonality and divisibility are two important properties of linear codes. It is interesting to establish relationship between them. By the well-known Gleason-Pierce-Ward Theorem, all self-dual divisible codes have been totally classified. However, the relationship between the self-orthogonality and divisibility of a q-ary linear codes is known only for$q=2,3$by Huffman and Pless in 2003. It has remained open for more than 20 years to consider other cases. The purpose of this paper is to settle this open problem under certain conditions and construct new families of self-orthogonal codes. Let q be a power of an odd prime p. Firstly, we prove that any p-divisible code containing the all-1 vector over the finite field${\mathbb {F}}_{q}$is self-orthogonal. More generally, it is concluded that any p-divisible$[n,k]$linear code over${\mathbb {F}}_{q}$containing codewords of weight n is monomially equivalent to an$[n,k]$self-orthogonal code over${\mathbb {F}}_{q}$. This result provides a very efficient way to find self-orthogonal codes from p-divisible codes. Secondly, we apply this result to construct self-orthogonal codes with excellent parameters or nice applications. For one thing, we use this result to study the self-orthogonality of generalized Reed-Muller codes, certain projective two-weight codes, and Griesmer codes. For another thing, by this useful result as well as the extending and augmentation techniques for linear codes, we construct eight new families of self-orthogonal divisible codes. These self-orthogonal codes and their duals contain many optimal or almost optimal codes. Besides, some self-orthogonal codes support combinatorial designs and some of them are proved to be optimal or almost optimal locally recoverable codes.

With the development of communication and Internet of Vehicles (IoV) technology, a large number of high precision sensors and computing units are widely used and deployed on vehicles. With the vehicles work as users, Mobile Crowdsensing (MCS) system has a broad application prospect in traffic planning, environmental monitoring and so on. The realization of these applications needs a large amount of data. However, in the process of crowdsensing, users are often faced with the consumption of computing, communication and energy and the risk of privacy leakage, so they are reluctant to actively participate. Therefore, we need to design a safe and reasonable incentive mechanism. In this paper, we focus on privacy protection and user incentive, and propose a framework of the vehicular crowdsensing with blockchain, as well as the smart contacts deployed on the blockchain. The characteristics of the blockchain are used to solve the security problems in the crowdsensing process. In addition, we propose a reverse auction-based incentive mechanism. A group of users with the highest reputation value are selected to complete the sensing tasks, and the payoffs are assigned according to the quality of the sensing data uploaded by the selected users. Finally, Matlab-based simulation verifies the effectiveness of the incentive mechanism proposed in this paper.

Ensuring the fairness and non-repudiation in the security exchange protocol of web service is critical. Model checking is often used for automatic verification for the security properties of protocol. However, the current model checker tools cannot support formalizing protocols with cryptographic primitives, specifying properties with linear temporal logic (LTL) and automatically generating resilient intruder model simultaneously and the application range of them is severely limited. To solve this problem, a model checker Fepchecker is proposed to verify the fairness and non-repudiation properties, which are critical features in security exchange protocols. Firstly, applied pi-calculus is extended to specify the protocols, and the LTL assertion is used for precisely describing fairness and non-repudiation. Secondly, an intruder model is applied to construct their behavior sequences automatically and the protocol sessions and message pattern are used to alleviate the states explosion problem. Thirdly, in our model checking algorithm, the fairness and non-repudiation properties are verified based on Labeled Transition System (LTS) semantics model and the MakeOneMove method is used to explore the state space on-the-fly in the verification process. Finally, Fepchecker is applied to verify six representative protocols and the results show that Fepchecker can effectively verify their fairness and non-repudiation properties.