Information on Result #1553363
Linear OOA(7106, 5764851, F7, 3, 15) (dual of [(5764851, 3), 17294447, 16]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(7106, 5764851, F7, 15) (dual of [5764851, 5764745, 16]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(7105, 5764849, F7, 15) (dual of [5764849, 5764744, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(8) [i] based on
- linear OA(797, 5764801, F7, 15) (dual of [5764801, 5764704, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(757, 5764801, F7, 9) (dual of [5764801, 5764744, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(78, 48, F7, 5) (dual of [48, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(78, 50, F7, 5) (dual of [50, 42, 6]-code), using
- a “Gra†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(78, 50, F7, 5) (dual of [50, 42, 6]-code), using
- construction X applied to Ce(14) ⊂ Ce(8) [i] based on
- linear OA(7105, 5764850, F7, 14) (dual of [5764850, 5764745, 15]-code), using Gilbert–Varšamov bound and bm = 7105 > Vbs−1(k−1) = 16290 086723 548156 402074 007130 010626 703129 014447 549105 818251 508002 344917 311556 601925 740935 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(7105, 5764849, F7, 15) (dual of [5764849, 5764744, 16]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(7106, 1921616, F7, 21, 15) (dual of [(1921616, 21), 40353830, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |