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On the Extended Lee Weights Modulo 2e of Linear Codes Over Z2

Bahattin Yilzid1, Zeynep Ödemis Özger2
1DEPARTMENT OF MATHEMaTiCs, FaTin University 34500 IsTanBuL, TURKEY
2DEPARTMENT OF ENGINEERING Sciences, izmir KAtip Cecest University, 35620 Izmir, TURKEY

Abstract

In this work, linear codes over Z2s are considered together with the extended Lee weight, which is defined as
wL(a)={aif a2s1,2sxif a>2s1.
The ideas used by Wilson and Yildiz are employed to obtain divisibility properties for sums involving binomial coefficients and the extended Lee weight. These results are then used to find bounds on the power of 2 that divides the number of codewords whose Lee weights fall in the same congruence class modulo 2e. Comparisons are made with the results for the trivial code and the results for the homogeneous weight.