Information on Result #1729307
Linear OOA(8173, 419441, F8, 33, 27) (dual of [(419441, 33), 13841380, 28]-NRT-code), using OOA 5-folding and stacking with additional row based on linear OOA(8173, 2097206, F8, 3, 27) (dual of [(2097206, 3), 6291445, 28]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8173, 2097206, F8, 27) (dual of [2097206, 2097033, 28]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8172, 2097204, F8, 27) (dual of [2097204, 2097032, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(19) [i] based on
- linear OA(8162, 2097152, F8, 27) (dual of [2097152, 2096990, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(810, 52, F8, 6) (dual of [52, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- construction X applied to Ce(26) ⊂ Ce(19) [i] based on
- linear OA(8172, 2097205, F8, 26) (dual of [2097205, 2097033, 27]-code), using Gilbert–Varšamov bound and bm = 8172 > Vbs−1(k−1) = 9500 815193 014620 997069 268746 727933 157413 684673 545155 958853 272828 168507 691871 221601 046024 092865 757511 128287 613836 009924 065728 266684 400524 396964 434189 400892 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(8172, 2097204, F8, 27) (dual of [2097204, 2097032, 28]-code), using
- construction X with Varšamov bound [i] based on
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 (146, 173, 419441)-net over F8 | [i] | Net Defined by OOA | |