Some new resolvable group divisible designs

Structured LDPC codes have been constructed using balanced incomplete block (BIB) designs, resolvable BIB designs, mutually orthogonal Latin rectangles, partial geometries, group divisible designs, resolvable group divisible designs and finite geometries. Here we have constructed LDPC codes from α – resolvable BIB and Group divisible designs. The sub–matrices of incidence matrix of such block design are used as a parity – check matrix of the code which satisfy row – column constraint. Here the girth of the proposed code is at least six and the corresponding LDPC code (or Tanner graph) is free of 4– cycles.

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A survey on resolvable group divisible designs with block size four

Discrete Mathematics ◽

10.1016/s0012-365x(03)00274-7 ◽

2004 ◽

Vol 279 (1-3) ◽

pp. 225-245 ◽

Cited By ~ 23

Author(s):

Gennian Ge ◽

Alan C.H Ling

Keyword(s):

Block Size ◽

Group Divisible Designs ◽

Group Divisible ◽

Resolvable Group

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Frames with Block Size Four

Canadian Journal of Mathematics ◽

10.4153/cjm-1992-063-x ◽

1992 ◽

Vol 44 (5) ◽

pp. 1030-1049 ◽

Cited By ~ 40

Author(s):

Rolf S. Rees ◽

Douglas R. Stinson

Keyword(s):

Group Size ◽

Block Size ◽

List Type ◽

Combinatorial Designs ◽

Recursive Construction ◽

Type Number ◽

Group Divisible Designs ◽

Group Divisible ◽

Resolvable Group

AbstractWe investigate the spectrum for frames with block size four, and discuss several applications to the construction of other combinatorial designs.Our main result is that a frame of type hu, having blocks of size four, exists if and only if u ≥ 5, h ≡ 0 mod 3 and h(u — 1) ≡ 0 mod 4, except possibly where(i)h = 9 and u ∈ ﹛13,17,29,33,93,113,133,153,173,193﹜;(ii)h ≡ 0 mod 12 and u ∈ ﹛8,12﹜,h = 36 and u ∈ ﹛7,18,23,28,33,38,43,48﹜,h = 24 or 120 and u ∈ ﹛7﹜,h = 72 and u ∈ 2Z+ U ﹛n : n ≡ 3 mod4 and n ≤527﹜ U ﹛563﹜; or(iii)h ≡ 6mod l2 and u ∈ (﹛17,29,33,563﹜ U ﹛n : n ≡ 3 or 11 mod 12 and n ≤ 527﹜ U ﹛n : n ≡ 7 mod 12 and n ≤ 259﹜), h = 18.Additionally, we give a new recursive construction for resolvable group-divisible designs from frames: if there is a resolvable k-GDD of type gu, a k-frame of type ﹛mg)v where u ≥ m + 1, and a resolvable TD(k, mv) then there is a resolvable k-GDD of type (mg)uv. We use this to construct some new resolvable GDDs with group size three and block size four.

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