A new proof of Delsarte, Goethals and Mac Williams theorem on minimal weight codewords of generalized Reed-Muller code
نویسنده
چکیده
We give a new proof of Delsarte, Goethals and Mac williams theorem on minimal weight codewords of generalized Reed-Muller codes published in 1970. To prove this theorem, we consider intersection of support of minimal weight codewords with affine hyperplanes and we proceed by recursion.
منابع مشابه
A new proof of Delsarte, Goethals and Mac Williams theorem on minimal weight codewords of generalized Reed-Muller codes
We give a new proof of Delsarte, Goethals and Mac williams theorem on minimal weight codewords of generalized Reed-Muller codes published in 1970. To prove this theorem, we consider intersection of support of minimal weight codewords with affine hyperplanes and we proceed by recursion.
متن کاملThe automorphism group of Generalized Reed-Muller codes
Berger, T. and P. Charpin, The automorphism group of Generalized Reed-Muller codes, Discrete Mathematics 117 (1993) l-17. We prove that the automorphism group of Generalized Reed-Muller codes is the general linear nonhomogeneous group. The Generalized Reed-Muller codes are introduced by Kasami, Lin and Peterson. An extensive study was made by Delsarte, Goethals and Mac-Williams; our result foll...
متن کاملReed Muller Sensing Matrices and the LASSO
We construct two families of deterministic sensing matrices where the columns are obtained by exponentiating codewords in the quaternary Delsarte-Goethals code DG(m, r). This method of construction results in sensing matrices with low coherence and spectral norm. The first family, which we call Delsarte-Goethals frames, are 2 dimensional tight frames with redundancy 2. The second family, which ...
متن کاملOn Low Weight Codewords of Generalized Affine and Projective Reed - Muller Codes ( Extended abstract )
We propose new results on low weight codewords of affine and projective generalized Reed-Muller codes. In the affine case we give some results on codewords that cannot reach the second weight also called the next to minimal distance. In the projective case the second distance of generalized Reed-Muller codes is estimated, namely a lower bound and an upper bound of this weight are given.
متن کاملMinimal/nonminimal codewords in the second order binary Reed-Muller codes: revisited
The result on the weight distribution of minimal codewords in the second order binary Reed-Muller code RM(2, m), was announced for the first time by Ashikhmin and Barg at ACCT’94. They gave only a sketch of the proof and later on a short and nice complete proof of geometric nature was exhibited in their paper: A. Ashikhmin and A. Barg, ”Minimal Vectors in Linear Codes”, IEEE Trans. on Informati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1001.2554 شماره
صفحات -
تاریخ انتشار 2010