Information on Result #1559408
Linear OOA(8173, 2097206, F8, 3, 27) (dual of [(2097206, 3), 6291445, 28]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound 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
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8173, 419441, F8, 33, 27) (dual of [(419441, 33), 13841380, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |