Permutation decoding for binary codes from lattice graphs
نویسندگان
چکیده
By finding explicit PD sets, we show that permutation decoding can be used for the binary code obtained from the row span over the field F2 of an adjacency matrix of the lattice graph L2(n) for any n 5. © 2007 Elsevier B.V. All rights reserved.
منابع مشابه
Binary codes from rectangular lattice graphs and permutation decoding
We examine the binary codes obtained from the row span over the field F2 of an adjacency matrix of the rectangular lattice graphs L2(m,n) for 3 ≤ m < n and show that permutation decoding can be used for full error-correction for these codes by finding explicit information sets and PD-sets for these information sets.
متن کاملNon-binary codes associated with triangular graphs, and permutation decoding
Non-binary codes of length ( n 2 ) , dimension n or n − 1, minimum weight n − 1 or 2n − 4, respectively, that can be obtained from designs associated with the complete graph on n vertices and their line graphs, the triangular graphs, are examined. The parameters of the codes and their automorphism groups for any odd prime are obtained and PD-sets inside the symmetric group Sn are found for full...
متن کاملNew Binary Constant Weight Codes Based on Cayley Graphs of Groups and Their Decoding Methods
We propose a new class of binary nonlinear codes of constant weights derived from a permutation representation of a group that is given by a combinatorial definition such as Cayley graphs of a group. These codes are constructed by the following direct interpretation method from a group: (1) take one discrete group whose elements are defined by generators and their relations, such as those in th...
متن کاملBinary codes from graphs on triples and permutation decoding
We show that permutation decoding can be used, and give explicit PD-sets in the symmetric group, for some of the binary codes obtained from the adjacency matrices of the graphs on ` n 3 ́ vertices, for n ≥ 7, with adjacency defined by the vertices as 3-sets being adjacent if they have zero, one or two elements in common, respectively.
متن کاملCodes from lattice and related graphs, and permutation decoding
Codes of length n and dimension 2n− 1 or 2n− 2 over the field Fp, for any prime p, that can be obtained from designs associated with the complete bipartite graph Kn,n and its line graph, the lattice graph, are examined. The parameters of the codes for all primes are obtained and PD-sets are found for full permutation decoding for all integers n ≥ 3.
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:
- Discrete Mathematics
دوره 308 شماره
صفحات -
تاریخ انتشار 2008