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The Automorphism Group of Linear Code

Author: QuLiJin
Tutor: LiuHongWei
School: Central China Normal University
Course: Applied Mathematics
Keywords: Linear code System code Finite field Automorphism group of a linear code Automorphism group of the linear weight code
CLC: O157.4
Type: Master's thesis
Year: 2007
Downloads: 29
Quote: 0
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Abstract


Automorphism group of a linear code is a basic research in algebraic coding , it cryptosystem design and analysis are important foundation for the design of the decoding algorithm . In general , however , seek the automorphism group of a linear code is very difficult . In the literature [ 18 ] and [ 20 ] , using the matrix generalized inverse theory given quite valid conclusions . Nevertheless, as in the code theory , the general amount of calculation is very large , it is necessary to the above conclusion for further study and simplified to reduce the computational workload . This article in the literature [ 12] , [ 19 ] , [ 21 ] on the basis of further research automorphism group of a linear code to obtain the following results : 1 . Using the binary case , the automorphism group of the linear weight code with its dual code automorphism group of the same nature , according to the nature of the matrix of the linear code inspection simplified since the calculation of the automorphism group . 2. Given automorphism group of any finite field linear weight code . 3. Arbitrary linear code is equivalent to the system code such as the price tag of the automorphism group isomorphic nature , more simplify the calculation of the automorphism group .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Coding theory ( on behalf of the digital theory )
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