Information on Result #1731881
Linear OOA(977, 4378, F9, 21, 19) (dual of [(4378, 21), 91861, 20]-NRT-code), using OOA 3-folding and stacking with additional row based on linear OOA(977, 13135, F9, 3, 19) (dual of [(13135, 3), 39328, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(977, 13136, F9, 3, 19) (dual of [(13136, 3), 39331, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(977, 13136, F9, 19) (dual of [13136, 13059, 20]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(976, 13134, F9, 19) (dual of [13134, 13058, 20]-code), using
- trace code [i] based on linear OA(8138, 6567, F81, 19) (dual of [6567, 6529, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(8133, 6562, F81, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- trace code [i] based on linear OA(8138, 6567, F81, 19) (dual of [6567, 6529, 20]-code), using
- linear OA(976, 13135, F9, 18) (dual of [13135, 13059, 19]-code), using Gilbert–Varšamov bound and bm = 976 > Vbs−1(k−1) = 64533 007435 981594 478124 168139 266388 015232 798430 043813 615160 566038 237489 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(976, 13134, F9, 19) (dual of [13134, 13058, 20]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(977, 13136, F9, 19) (dual of [13136, 13059, 20]-code), using
Mode: Linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (58, 77, 4378)-net over F9 | [i] | Net Defined by OOA | |