Improvements on the Johnson bound for Reed–Solomon codes
نویسندگان
چکیده
منابع مشابه
Improvements on the Johnson bound for Reed-Solomon codes
For Reed-Solomon Codes with block length n and dimension k, the Johnson theorem states that for a Hamming ball of radius smaller than n − √ nk, there can be at most O(n) codewords. It was not known whether for larger radius, the number of code words is polynomial. The best known list decoding algorithm for Reed-Solomon Codes due to Guruswami and Sudan [13] is also known to work in polynomial ti...
متن کاملFurther improvements on the Feng-Rao bound for dual codes
Salazar, Dunn and Graham in [15] presented an improved Feng-Rao bound for the minimum distance of dual codes. In this work we take the improvement a step further. Both the original bound by Salazar et. al., as well as our improvement are lifted so that they deal with generalized Hamming weights. We also demonstrate the advantage of working with one-way well-behaving pairs rather than weakly wel...
متن کاملAn improvement of the Johnson bound for subspace codes
Subspace codes, i.e., subset of a finite-field Grassmannian, are applied in random linear network coding. Here we give improved upper bounds based on the Johnson bound and a connection to divisible codes, which is presented in a purely geometrical way. This complements a recent approach for upper bounds on the maximum size of partial spreads based on projective qr-divisible codes.
متن کاملOn the Failing Cases of the Johnson Bound for Error-Correcting Codes
A central problem in coding theory is to determine Aq(n, 2e + 1), the maximal cardinality of a q-ary code of length n correcting up to e errors. When e is fixed and n is large, the best upper bound for A(n, 2e+1) (the binary case) is the well-known Johnson bound from 1962. This however simply reduces to the sphere-packing bound if a Steiner system S(e + 1, 2e + 1, n) exists. Despite the fact th...
متن کاملOn Perfect Codes in the Johnson Graph
In this paper we consider the existence of nontrivial perfect codes in the Johnson graph J(n, w). We present combinatorial and number theory techniques to provide necessary conditions for existence of such codes and reduce the range of parameters in which 1-perfect and 2-perfect codes may exist.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2008.06.014