Results 1  10
of
143,224
Long Nonbinary Codes Exceeding the Gilbert–Varshamov Bound for any Fixed Distance
"... Abstract—Let @ A denote the maximum size of aary code of length and distance. We study the minimum asymptotic redundancy @ Aa �� � @ A as grows while and are fixed. For any and I, long algebraic codes are designed that improve on the Bose–Chaudhuri–Hocquenghem (BCH) codes and have the lowest asymp ..."
Abstract
 Add to MetaCart
asymptotic redundancy @ A @ @ QA C I @ PAA ��� known to date. Prior to this work, codes of fixed distance that asymptotically surpass BCH codes and the Gilbert–Varshamov bound were designed only for distances R S and T. Index Terms—Affine lines, Bose–Chaudhuri–Hocquenghem (BCH) code, Bezout’s theorem, norm.
Long Nonbinary Codes Exceeding the GilbertVarshamov bound for Any Fixed Distance
"... Abstract — Let ¢¡¤£¦¥¨§©¥��¦ � denote the maximum size of a £ary code of length § asymptotic � redundancy and distance � ..."
Abstract
 Add to MetaCart
Abstract — Let ¢¡¤£¦¥¨§©¥��¦ � denote the maximum size of a £ary code of length § asymptotic � redundancy and distance �
Long Nonbinary Codes Exceeding the GilbertVarshamov Bound for . . .
 IEEE TRANS. INFORM. THEORY
, 2004
"... Let A(q; n; d) denote the maximum size of a q ary code of length n and distance d. We study the minimum asymptotic redundancy (q; n; d) = n log q A(q; n; d) as n grows while q and d are fixed. For any d and q d 1; long algebraic codes are designed that improve on the BCH codes and have the lowest ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
asymptotic redundancy (q; n; d) . ((d 3) + 1=(d 2)) log q n known to date. Prior to this work, codes of fixed distance that asymptotically surpass BCH codes and the GilbertVarshamov bound were designed only for distances 4; 5; and 6.
Strengthening the VarshamovGilbert bound
, 1998
"... The paper discusses some ways to strengthen (nonasymptotically) the GilbertVarshamov bound for linear codes. The unifying idea is to study a certain graph constructed on vectors of low weight in the cosets of the code, which we call the Varshamov graph. Various simple estimates of the number of its ..."
Abstract
 Add to MetaCart
The paper discusses some ways to strengthen (nonasymptotically) the GilbertVarshamov bound for linear codes. The unifying idea is to study a certain graph constructed on vectors of low weight in the cosets of the code, which we call the Varshamov graph. Various simple estimates of the number
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
Abstract

Cited by 741 (23 self)
 Add to MetaCart
but also for any channel with symmetric stationary ergodic noise. We give experimental results for binarysymmetric channels and Gaussian channels demonstrating that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed
On GilbertVarshamov type bounds for
"... In this paper we derive a GilbertVarshamov type bound for linear codes over Galois rings GR(p l ; j): However, this bound does not guarantee existence of better linear codes over GR(p l ; j) than the usual GilbertVarshamov bound for linear codes over the residue class field GR(p j ): Next ..."
Abstract
 Add to MetaCart
In this paper we derive a GilbertVarshamov type bound for linear codes over Galois rings GR(p l ; j): However, this bound does not guarantee existence of better linear codes over GR(p l ; j) than the usual GilbertVarshamov bound for linear codes over the residue class field GR(p j
Asymptotic improvement of the GilbertVarshamov bound for linear codes
 ISIT 2006
, 2006
"... The GilbertVarshamov bound states that the maximum size A2(n, d) of a binary code of length n and minimum distance d satisfies A2(n, d) ≥ 2n /V (n, d −1) where V (n, d) = ∑d n i=0 i stands for the volume of a Hamming ball of radius d. Recently Jiang and Vardy showed that for binary nonlinear code ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
The GilbertVarshamov bound states that the maximum size A2(n, d) of a binary code of length n and minimum distance d satisfies A2(n, d) ≥ 2n /V (n, d −1) where V (n, d) = ∑d n i=0 i stands for the volume of a Hamming ball of radius d. Recently Jiang and Vardy showed that for binary non
On the GilbertVarshamov distance of Abelian group codes
"... Abstract — The problem of the minimum Bhattacharyya distance of group codes over symmetric channels is addressed. Ensembles of Zmlinear codes are introduced and their typical minimum distance characterized in terms of the GilbertVarshamov distances associated to the subgroups of Zm. For the AWGN ..."
Abstract
 Add to MetaCart
Abstract — The problem of the minimum Bhattacharyya distance of group codes over symmetric channels is addressed. Ensembles of Zmlinear codes are introduced and their typical minimum distance characterized in terms of the GilbertVarshamov distances associated to the subgroups of Zm
VARSHAMOVGILBERT BOUNDS FOR PARTITION CODES
"... Partition codes characterize the partitioning of n elements into q partitions, with 2≤q<n. The space generated by such codes is nonhomogeneous, resulting in the inability to define a closed formula for determining the volume of a sphere for various n and q. With the use of a Java program develope ..."
Abstract
 Add to MetaCart
developed by the team, we calculate the VarshamovGilbert bounds as generated from the average sphere volume for various values of n and q. 2. Statement of the Problem Partition codes have the potential to be applicable for many societal needs, most notably the diagnosis of mental impairments in youth. One
Results 1  10
of
143,224