A deterministic algorithm for the distance and weight distribution of binary nonlinear codes
نویسندگان
چکیده
Given a binary nonlinear code, we provide a deterministic algorithm to compute its weight and distance distribution, and in particular its minimum weight and its minimum distance, which takes advantage of fast Fourier techniques. This algorithm’s performance is similar to that of best-known algorithms for the average case, while it is especially efficient for codes with low information rate. We provide complexity estimates for several cases of interest.
منابع مشابه
A probabilistic algorithm for computing minimum weights of large error-correcting codes
Given a binary nonlinear code, we provide a deterministic algorithm to to use probabilistic algorithms for the computation of the minimum distance, such as the there are algorithms which perform much better than brute force, e.g. code with large minimum distance and the minimum weight, of any random binary code. code C over Fq of length n and dimension k capable of correction w errors. A matrix...
متن کاملMinimum Distance of Binary Nonlinear Codes∗
A binary nonlinear code can be represented as the union of cosets of a binary linear subcode. Using this representation, new algorithms methods to compute the minimum Hamming weight and distance are presented. The performance of these algorithms is also studied.
متن کاملLinear Codes over Galois Ring GR(p2, r) Related to Gauss sums
Linear codes over finite rings become one of hot topics in coding theory after Hommons et al.([4], 1994) discovered that several remarkable nonlinear binary codes with some linear-like properties are the images of Gray map of linear codes over Z4. In this paper we consider two series of linear codes C(G) and C̃(G) over Galois ring R = GR(p2,r), where G is a subgroup of R(s) ∗ and R(s) = GR(p2,rs...
متن کاملA classification of binary systematic codes of small defect
In this paper non-trivial non-linear binary systematic AMDS codes are classified in terms of their weight distributions, employing only elementary techniques. In particular, we show that their length and minimum distance completely determine the weight distribution.
متن کاملDetermination of the Equilibrium Parameters of Gaseous Detonations Using a Genetic Algorithm
The present work is concerned with the development of a new algorithm for determination of the equilibrium composition of gaseous detonations. The elements balance equations, and the second law of thermodynamics (i.e., the minimization of the Gibbs free energy of products), are used to determine the equilibrium composition of the detonation products. To minimize the Gibbs free energy with tradi...
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/1505.00542 شماره
صفحات -
تاریخ انتشار 2015