Information on Result #1442764
Linear OOA(7104, 16841, F7, 2, 23) (dual of [(16841, 2), 33578, 24]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(7104, 16841, F7, 23) (dual of [16841, 16737, 24]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(7103, 16839, F7, 23) (dual of [16839, 16736, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(796, 16807, F7, 23) (dual of [16807, 16711, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(771, 16807, F7, 17) (dual of [16807, 16736, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(77, 32, F7, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(7103, 16840, F7, 22) (dual of [16840, 16737, 23]-code), using Gilbert–Varšamov bound and bm = 7103 > Vbs−1(k−1) = 23 996431 312305 172653 319647 709054 911929 803346 902005 309521 315644 523170 661060 501274 527479 [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(7103, 16839, F7, 23) (dual of [16839, 16736, 24]-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(7104, 8420, F7, 3, 23) (dual of [(8420, 3), 25156, 24]-NRT-code) | [i] | OOA Folding | |