Information on Result #1713852
Digital (141, 158, 691983)-net over F3, using net defined by OOA based on linear OOA(3158, 691983, F3, 20, 17) (dual of [(691983, 20), 13839502, 18]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3158, 1383967, F3, 4, 17) (dual of [(1383967, 4), 5535710, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3158, 1383967, F3, 3, 17) (dual of [(1383967, 3), 4151743, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3158, 1594328, F3, 3, 17) (dual of [(1594328, 3), 4782826, 18]-NRT-code), using
- 32 times duplication [i] based on linear OOA(3156, 1594328, F3, 3, 17) (dual of [(1594328, 3), 4782828, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3156, 4782984, F3, 17) (dual of [4782984, 4782828, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3155, 4782983, F3, 17) (dual of [4782983, 4782828, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3155, 4782983, F3, 17) (dual of [4782983, 4782828, 18]-code), using
- OOA 3-folding [i] based on linear OA(3156, 4782984, F3, 17) (dual of [4782984, 4782828, 18]-code), using
- 32 times duplication [i] based on linear OOA(3156, 1594328, F3, 3, 17) (dual of [(1594328, 3), 4782828, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3158, 1594328, F3, 3, 17) (dual of [(1594328, 3), 4782826, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3158, 1383967, F3, 3, 17) (dual of [(1383967, 3), 4151743, 18]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.