Information on Result #1449932
Linear OOA(981, 6578, F9, 2, 22) (dual of [(6578, 2), 13075, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(981, 6578, F9, 22) (dual of [6578, 6497, 23]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(980, 6576, F9, 22) (dual of [6576, 6496, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(977, 6561, F9, 22) (dual of [6561, 6484, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(965, 6561, F9, 19) (dual of [6561, 6496, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 94−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(93, 15, F9, 2) (dual of [15, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(980, 6577, F9, 21) (dual of [6577, 6497, 22]-code), using Gilbert–Varšamov bound and bm = 980 > Vbs−1(k−1) = 10532 133580 878318 518312 656330 986688 734757 347975 912796 678268 845108 821558 040449 [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(980, 6576, F9, 22) (dual of [6576, 6496, 23]-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(981, 3289, F9, 3, 22) (dual of [(3289, 3), 9786, 23]-NRT-code) | [i] | OOA Folding | |