Some new binary codes with improved minimum distances
نویسنده
چکیده
It has been well-known that the class of quasi-cyclic (QC) codes contain many good codes. In this paper, a method to conduct a computer search for binary 2-generator QC codes is presented, and a large number of good 2-generator QC codes have been obtained. 5 new binary QC codes that improve the lower bounds on minimum distance are presented. Furthermore, with new 2-generator QC codes and Construction X, 2 new improved binary linear codes are obtained. With the standard construction techniques, another 16 new binary linear codes that improve the lower bound on the minimum distance have also been obtained. 2010 MSC: 94B05, 94B65
منابع مشابه
On the Minimum Distance of Some Families of Z2k-Linear Codes
With the help of a computer, we obtain the minimum distance of some codes belonging to two families of Z2k -linear codes: the first is the generalized Kerdock codes which aren’t as good as the best linear codes and the second is the Hensel lift of quadratic residue codes. In the latter, we found new codes with same minimum distances as the best linear codes of same length and same cardinality. ...
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 کاملMultilevel Input Ring-Tcm Coding Scheme: a Method for Generating High-Rate Codes
The capability of multilevel input ring-TCM coding scheme for generating high-rate codes with improved symbol Hamming and squared Euclidean distances is demonstrated. The existence of uniform codes and the decoder complexity are also considered.
متن کاملOn Upper Bounds for Minimum Distances and Covering Radius of Non-binary Codes
We consider upper bounds on two fundamental parameters of a code; minimum distance and covering radius. New upper bounds on the covering radius of non-binary linear codes are derived by generalizing a method due to S. Litsyn and A. Tiett avv ainen 10] and combining it with a new upper bound on the asymptotic information rate of non-binary codes. The new upper bound on the information rate is an...
متن کاملWoven Codes with Outer Block Codes
Woven codes with outer binary block codes and additional permutation are presented. This enables the construction of a new class of woven block codes, where the minimum distance is about twice the product of the minimum distances of the component codes.
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:
دوره شماره
صفحات -
تاریخ انتشار 2018