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|1. (WO2017041232) ENCODING AND DECODING FRAMEWORK FOR BINARY CYCLIC CODE|
|Applicants:||GUANGDONG SUPER COMPUTING & DATA ASSURANCE TECHNOLOGY CO., LTD
LI, Shuoyen Robert
SHUN, Kenneth W.
|Title:||ENCODING AND DECODING FRAMEWORK FOR BINARY CYCLIC CODE|
The present invention relates to the field of distributed storage systems. Disclosed is an encoding and decoding framework for a binary cyclic code, the framework consisting of a linear code and an alphabet. The linear code is a binary cyclic code, the binary cyclic code is an Rm-based linear code, and a binary parity-check code Cm is used as the alphabet, wherein Rm is a polynomial ring, a variable z represents a cyclic right shift operation of the ring Rm, and Cm consists of an even number of nonzero coefficient polynomials. In a binary-based finite field F2, the parity-check code Cm has a dimension of m-1, and Cm has a check polynomial of h(z):=1+z+…+zm-1. The present invention has the following beneficial effects: Because the encoding and decoding processes of the binary cyclic code both involve an exclusive-or operation only and have low computation complexity and small computation overheads, the present invention can greatly reduce the system computation delay, save time and resources, and reduce the costs, and is suitable for actual storage systems. The present invention provides necessary and sufficient conditions under which the binary cyclic code satisfies an MDS property, which is an important theoretical basis for designing an MDS code with low computation complexity.