Codes associated with triangular graphs and permutation decoding
نویسندگان
چکیده
Linear codes that can be obtained from designs associated with the complete graph onnvertices and its line graph, the triangular graph, are examined. The codes have length n choose 2, dimension n or n − 1, and minimum weight n− 1 or 2n− 4. 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 permutation decoding for all primes and all integers n ≥ 6.
منابع مشابه
Non-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 کاملPermutation decoding for the binary codes from triangular graphs
By finding explicit PD-sets we show that permutation decoding can be used for the binary code obtained from an adjacency matrix of the triangular graph T (n) for any n ≥ 5.
متن کاملPartial permutation decoding for codes from Paley
We examine codes from the Paley graphs for the purpose of permutation decoding and observe that after a certain length, PD-sets to correct errors up to the code’s error-capability will not exist. In this paper we construct small sets of permutations for correcting two errors by permutation decoding for the case where the codes have prime length.
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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IJICoT
دوره 1 شماره
صفحات -
تاریخ انتشار 2010