2009
DOI: 10.1007/s10801-009-0191-2
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Bounds on permutation codes of distance four

Abstract: A permutation code of length n and distance d is a set of permutations from some fixed set of n symbols such that the Hamming distance between each distinct x, y ∈ is at least d. In this note, we determine some new results on the maximum size of a permutation code with distance equal to 4, the smallest interesting value. The upper bound is improved for almost all n via an optimization problem on Young diagrams. A new recursive construction improves known lower bounds for small values of n.

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Cited by 24 publications
(15 citation statements)
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“…In fact, not much progress has been made for , except for the small lengths. Therefore, most efforts are focused on seeking good upper or lower bounds for (see [3], [6], [7], [10], and the references therein). The following are some well-known elementary consequences by basic combinatorial techniques.…”
Section: Some Known Boundsmentioning
confidence: 99%
See 1 more Smart Citation
“…In fact, not much progress has been made for , except for the small lengths. Therefore, most efforts are focused on seeking good upper or lower bounds for (see [3], [6], [7], [10], and the references therein). The following are some well-known elementary consequences by basic combinatorial techniques.…”
Section: Some Known Boundsmentioning
confidence: 99%
“…Using linear programming and representation theory of the characters of , Dukes and Sawchuck [7] improve the upper bound on the special case as follows. Theorem 3: If for some integer , then…”
Section: The Cardinality Of Ismentioning
confidence: 99%
“…Unmarked entries UB Taken from [11] or old LB Superscript a Taken from [7] Superscript b Taken from [8] Superscript c Taken from [9] Superscript d Taken from [16] Superscript e Upper bound taken from [22] Superscript f Taken from [10] Superscript g Upper bound taken from Theorem 3 of [11] Superscript h Upper bound taken from [3] at least d. The size of the largest clique (complete subgraph) in G(n, d) gives the value of M(n, d). When an automorphism group is used, clique search can be applied to a graph with vertices representing the orbits of the automorphism group.…”
Section: Maximum Clique Algorithmsmentioning
confidence: 99%
“…As well as white Gaussian noise the codes must combat permanent narrow band noise from electrical equipment or magnetic fields, and impulse noise. Most of the approaches presented in the literature are based on linear programming [7], [8] or on group theory ideas [7], [9], [10], [11], which have more recently been amalgamated with optimization, mainly based on search techniques [12], [13], [14].…”
Section: Introductionmentioning
confidence: 99%