Local Weight Distribution of the (256, 93) Third-Order Binary Reed-Muller Code
نویسندگان
چکیده
Local weight distribution is the weight distribution of minimal codewords in a linear code. We give the local weight distribution of the (256, 93) third-order binary Reed-Muller code. For the computation, a coset partitioning algorithm is modified by using a binary shift invariance property. This reduces the time complexity by about 1/256 for the code. A necessary and sufficient condition for minimality in Reed-Muller codes is also presented. key words: local weight distribution, minimal codeword, Reed-Muller code, binary shift
منابع مشابه
On binary codes related to mutually quasi-unbiased weighing matrices
Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying the conditions that the number of non-zero weights of the code is four and the code contains the first order Reed–Muller code. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes satisfying the conditions are determined. We also give ...
متن کاملRestrictions on the weight distribution of binary linear codes imposed by the structure of Reed-Muller codes
Abstmcf-The words of a binary linear [n,k] code C whose weights belong to a given subset I C { 0, 1,. .. , n} constitute a word in a certain Reed-Muller code !R!Dl ((r, k). Appropriate choices of I result in low values of the order r and thus yield restrictions on the weight distribution of C.
متن کاملOn the third weight of generalized Reed-Muller codes
In this paper, we study the third weight of generalized Reed-Muller codes. Using results from [6], we prove under some restrictive condition that the third weight of generalized Reed-Muller codes depends on the third weight of generalized Reed-Muller codes of small order with two variables. In some cases, we are able to determine the third weight and the third weight codewords of generalized Re...
متن کاملRestrictions on Weight Distribution of Reed-Muller Codes
I t is shown t h a t in the r t h order binary Reed-Muller code of length N = 2" and m i n i m u m distance d = 2~-L the only code-words having weight between d and 2d are those with weights of the form 2d-2 t for some i. The same result also holds for certain super-codes of the R M codes. DEFI~ITm~<. T h e weight of an integer k, W(/~), is the n u m b e r of l's in the binary expansion of ]~. ...
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:
- IEICE Transactions
دوره 90-A شماره
صفحات -
تاریخ انتشار 2007