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A perfect t -code in a graph Γ is a subset of V (Γ) such that every vertex of Γ is at a distance not more than t , to exactly one vertex of . In this paper, we present a new family of perfect t -codes in Cayley graphs of groups. We proposed the role of the subgroups of a group to create perfect t -codes by restricting the elements of the left transversal of the subgroups in the given group. Also, we introduce a new decoding algorithm for the all of perfect t -codes in Cayley graphs. These codes are able to correct every t -error pattern. [ABSTRACT FROM AUTHOR]

In securities trading, low latency helps investors take the leading position in the market. Conventionally, market data is decoded with software running on general computers. However, the serial structure of software and complex operating system scheduling cause high latency. This paper designs an accelerator for decoding market data based on field-programmable gate array (FPGA). We propose a pipeline in the accelerator, where every part works independently and parallelly. Furthermore, we present a mechanism for encoding templates, which avoids reconstructing the accelerator and decreases the cost when the template is renewed. We evaluate this accelerator with real Financial Information eXchange (FIX) messages and FIX Adapting for Streaming (FAST) templates, attaining an average latency of 447 ns. [ABSTRACT FROM AUTHOR]