Effective gamification can only be based on understanding the relationship between learner motivation and the game elements which are used to gamify learning activities. Although frequently mentioned, Virtual Currency (VC) remains underused and scarcely studied in educational gamification. As a motivational affordance, VC can be thought of as supporting different types of motivation, but currently, there is a lack of empirical studies which investigate this. Recognizing this gap, the purpose of our study was to empirically investigate whether and how gamifying learning activities with virtual currency can engender motivation for out-of-class practicing and what type of motivation. In the limited research others have conducted, VC has been studied largely in combination with other game elements, which does not allow reaching reliable conclusions about the impact of the individual elements. For this reason, we studied the effects of VC in a gamified Discrete Math course isolated from other game elements. The study showed that using VC to gamify practicing increased students’ practicing activity, which resulted in improved academic performance. The study also revealed that while gamified practicing did not increase students’ intrinsic motivation, it supported internalization of motivation towards this learning activity.

It has been proven in a series of works that the order of the automorphism group of a self-dual binary [72,36,16] code does not exceed five. Up to equivalence, we obtain a parametrization of all self-dual binary codes of length 72 with automorphism of order four, which can be extremal. We use extensive computations in Magma and on a supercomputer to show that the automorphism group of an extremal self-dual binary code of length 72 does not have an element of order four.

A long standing open question in coding theory is whether a binary self-dual [72,36,16] code exists. It was shown recently that the automorphism group order of such code is equal to 2imiddot3jmiddot5middot7, 2imiddot3jmiddot7, 2imiddot3jmiddot5, or 2imiddot3jfor some nonnegative integers i and j. We show that the group order is not a multiple of 35 and find that only 22 orders are possible

We find new extremal [76,38,14] and [78,39,14] binary self-dual codes. The code of length 76 is the first known self-dual code with these parameters. It is shadow extremal and the shortest known self-dual code with minimal distance 14. It has an automorphism of order 19 without fixed coordinates. The code of length 78 has a new weight enumerator and an automorphism of order 19 with two fixed coordinates.