Abstract
Recently, the fourth weight of generalized Reed-Muller codes Rq(a(q−1)+b,m) have been characterized for 3≤b<q+43 and 0≤a≤m−3. In this paper, we study the codewords reaching the fourth weight of generalized Reed-Muller codes. We will determine the fourth weight codewords of generalized Reed-Muller codes of order r=a(q−1)+b with 3≤b<q+43 and 0≤a≤m−3. Also, we characterize the number of fourth weight codewords of Rq(b,m) for 3≤b<q+43.
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