Constructions for Permutation Codes in Powerline Communications

Chu, Wensong; Colbourn, Charles J.; Dukes, Peter J.

doi:10.1023/b:desi.0000029212.52214.71

Cited by 145 publications

(187 citation statements)

References 12 publications

Supporting

Mentioning

187

Contrasting

Order By: Relevance

“…As we have seen in Lemma 1, when the PA is a group and some of its cosets, one need not check the distance between every pair of permutations and one can store the set of coset representatives instead of the set of all permutations. It is worth noting that in [5], the authors computed a PA of size 58,322 for M (16,9) and stated that this lower bound is not as good as what is given by the GV lower bound 3 . They stated, "...…”

Section: Resultsmentioning

confidence: 94%

“…It is also known that M(n, n − 1) ≥ kn, where k is the number of mutually orthogonal latin squares (MOLS) of order n [6], which means computing large collections of MOLS is related to searching for large permutation arrays. Other techniques that have been used include permutation polynomials [5], and special groups, such as the Mathieu groups M 22 , M 23 and M 24 [4].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Constructing permutation arrays from groups

Bereg

Levy

Sudborough

2017

Des. Codes Cryptogr.

View full text Add to dashboard Cite

Let M (n, d) be the maximum size of a permutation array on n symbols with pairwise Hamming distance at least d. We use various combinatorial, algebraic, and computational methods to improve lower bounds for M (n, d). We compute the Hamming distances of affine semilinear groups and projective semilinear groups, and unions of cosets of AGL(1, q) and P GL(2, q) with Frobenius maps to obtain new, improved lower bounds for M (n, d). We give new randomized algorithms. We give better lower bounds for M (n, d) also using new theorems concerning the contraction operation. For example, we prove a quadratic lower bound for M (n, n − 2) for all n ≡ 2 (mod 3) such that n + 1 is a prime power.

show abstract

Section: Resultsmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Constructing permutation arrays from groups

Bereg

Levy

Sudborough

2017

Des. Codes Cryptogr.

View full text Add to dashboard Cite

show abstract

“…Codes formed in this manner, called permutation codes, have more recently attracted attention due to their applications to powerline communications; see [17,20,30]. In [23], it is noted that a 2-GHD k (s, v; λ) is equivalent to a k-uniform PA(s, λ; v).…”

Section: Ghds Permutation Arrays and Codesmentioning

confidence: 99%

On generalized Howell designs with block size three

Abel

Bailey

Burgess

et al. 2015

Des. Codes Cryptogr.

View full text Add to dashboard Cite

In this paper, we examine a class of doubly resolvable combinatorial objects. Let t, k, λ, s and v be nonnegative integers, and let X be a set of v symbols. A generalized Howell design, denoted t-GHD k (s, v; λ), is an s × s array, each cell of which is either empty or contains a k-set of symbols from X, called a block, such that: (i) each symbol appears exactly once in each row and in each column (i.e. each row and column is a resolution of X); (ii) no t-subset of elements from X appears in more than λ cells. Particular instances of the parameters correspond to Howell designs, doubly resolvable balanced incomplete block designs (including Kirkman squares), doubly resolvable nearly Kirkman triple systems, and simple orthogonal multi-arrays (which themselves generalize mutually orthogonal Latin squares). Generalized Howell designs also have connections with permutation arrays and multiply constant-weight codes.In this paper, we concentrate on the case that t = 2, k = 3 and λ = 1, and write GHD(s, v). In this case, the number of empty cells in each row and column falls between 0 and (s−1)/3. Previous work has considered the existence of GHDs on either end of the spectrum, with at most 1 or at least (s − 2)/3 empty cells in each row or column. In the case of one empty cell, we correct some results of Wang and Du, and show that there exists a GHD(n + 1, 3n) if and only if n ≥ 6, except possibly for n = 6. In the case of two empty cells, we show that there exists a GHD(n + 2, 3n) if and only if n ≥ 6. Noting that the proportion of cells in a given row or column of a GHD(s, v) which are empty falls in the interval [0, 1/3), we prove that for any π ∈ [0, 5/18], there is a GHD(s, v) whose proportion of empty cells in a row or column is arbitrarily close to π.

show abstract

“…Permutation codes have received remarkable attention in the literature [1], [2], [3], [4], [5], [6], [7]. This happened because of their application to powerline communications when M-ary Frequency-Shift Keying modulation is used [8], [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Permutation Codes: a New Upper Bound for M(7,5)

2014

International Academy of Engineers (IA-E) Dec. 30-31, 2014 Bangkok, Thailand

View full text Add to dashboard Cite

Abstract-This paper deals with permutation codes. These codes have a main application in error correction in telecommunications. An algorithm based on combinatorial optimization concepts such as branch and bound, and graph theoretical concepts such as graph isomorphism, is discussed. The new theoretical result M(7,5) ≤ 122, obtained by this approach, is finally disclosed.Index Terms-Branch and bound algorithms, Permutation codes, Upper bounds.

show abstract

Constructions for Permutation Codes in Powerline Communications

Cited by 145 publications

References 12 publications

Constructing permutation arrays from groups

Constructing permutation arrays from groups

On generalized Howell designs with block size three

Permutation Codes: a New Upper Bound for M(7,5)

Contact Info

Product

Resources

About