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A generalisation of the GilbertVarshamov bound and its asymptotic evaluation
"... Abstract. The GilbertVarshamov (GV) lower bound on the maximum cardinality of a qary code of length n with minimum Hamming distance at least d can be obtained by application of Turán’s theorem to the graph with vertex set {0, 1,..., q − 1}n in which two vertices are joined if and only if their Ha ..."
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Abstract. The GilbertVarshamov (GV) lower bound on the maximum cardinality of a qary code of length n with minimum Hamming distance at least d can be obtained by application of Turán’s theorem to the graph with vertex set {0, 1,..., q − 1}n in which two vertices are joined if and only
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 ..."
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Cited by 13 (2 self)
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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 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 ..."
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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
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 ..."
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. For the AWGN channel with 8PSK as input it is shown that the typical Z8linear code achieves the GilbertVarshamov bound. I.
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 ..."
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Cited by 7 (1 self)
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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.
Improving the GilbertVarshamov bound for qary codes
 IEEE Trans. Inform. Theory
, 2005
"... Given positive integers q, n and d, denote by Aq(n, d) the maximum size of a qary code of length n and minimum distance d. The famous GilbertVarshamov bound asserts that where Vq(n, d) = P d i=0 Aq(n, d + 1) ≥ q n /Vq(n, d), ` ´ n i (q − 1) is the volume of a qary sphere of radius d. i Extendi ..."
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Cited by 11 (0 self)
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Given positive integers q, n and d, denote by Aq(n, d) the maximum size of a qary code of length n and minimum distance d. The famous GilbertVarshamov bound asserts that where Vq(n, d) = P d i=0 Aq(n, d + 1) ≥ q n /Vq(n, d), ` ´ n i (q − 1) is the volume of a qary sphere of radius d. i
A GILBERTVARSHAMOV TYPE BOUND FOR EUCLIDEAN PACKINGS.
"... Abstract. The present paper develops a method to obtain a GilbertVarshamov type bound for dense packings in the Euclidean spaces using suitable lattices. For the Leech lattice the obtained bounds are quite reasonable for large dimensions, better than the MinkowskiHlawka bound but not as good as th ..."
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Abstract. The present paper develops a method to obtain a GilbertVarshamov type bound for dense packings in the Euclidean spaces using suitable lattices. For the Leech lattice the obtained bounds are quite reasonable for large dimensions, better than the MinkowskiHlawka bound but not as good
Some notes on the binary GilbertVarshamov bound
"... Abstract. Given a linear code [n, k, d] with parity check matrix H, we provide inequality that supports existence of a code with parameters [n+ l + 1, k + l, d]. We show that this inequality is stronger than the GilbertVarshamov (GV) bound even if the existence of the code [n, k, d] is guaranteed b ..."
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Abstract. Given a linear code [n, k, d] with parity check matrix H, we provide inequality that supports existence of a code with parameters [n+ l + 1, k + l, d]. We show that this inequality is stronger than the GilbertVarshamov (GV) bound even if the existence of the code [n, k, d] is guaranteed
Asymptotic Improvement of the Gilbert–Varshamov Bound on the Size of Binary Codes
"... Abstract—Given positive integers and, let P @ A denote the maximum size of a binary code of length and minimum distance. The wellknown Gilbert–Varshamov bound asserts that P @ A P @ IA, where @ volume of a Hamming sphere of radius Aa aH is the. We show that, in fact, there exists a positive constan ..."
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Abstract—Given positive integers and, let P @ A denote the maximum size of a binary code of length and minimum distance. The wellknown Gilbert–Varshamov bound asserts that P @ A P @ IA, where @ volume of a Hamming sphere of radius Aa aH is the. We show that, in fact, there exists a positive
Results 1  10
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247,853