Generalized Pair Weights And Hamming Weight Distribution Of Outer Product Codes

In coding theory,it is a hot research topic to construct new codes by shorten-ing and extending the code length or combining existing codes.The outer product code is a new code constructed by linear codes,i.e.,the classical Reed-Muller codes R(1,m)can be viewed as outer product codes which is constructed by m linear codes F22 over F2.At the end of the last century,some scholars have studied the algebraic structures and minimal Hamming weights of outer product codes over finite fields.In particular,they obtained the result that the generalized Hamming weights of the outer product of two self-complementary codes can be obtained by the generalized Hamming weights of two self-complementary codes.Recently,Liu and Pan intro-duced the concept of the generalized pair weight of arbitrary linear code,moreover,they studied the properties of the generalized pair weights of linear codes.Particu-larly,they obtained the relationship between the generalized Hamming weights and the generalized pair weights of linear codes.The binary linear codes are widely used in practical communication.In this thesis,we study the generalized pair weights and Hamming weight distribution of binary outer product codes.We firstly study the highest order of the generalized pair weight of outer product of two linear codes,which can be determined by the code length,the generalized Hamming weights and the generalized pair weights of two linear codes,in addition,we obtain the pair weight hierarchy of outer product codes.Secondly,we get a necessary and sufficient condition of the outer product code to be a linear constant weight code,and we prove that the outer product code is a linear weakly constant weight code if and only if both two linear codes are linear weakly constant weight codes over the finite field F2.Finally,we give an algorithm to compute the weight distribution and weight enumerator of outer product codes over the finite field F2.