Information on Result #1560487
Linear OOA(983, 4782997, F9, 3, 13) (dual of [(4782997, 3), 14348908, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(983, 4782997, F9, 13) (dual of [4782997, 4782914, 14]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(981, 4782993, F9, 13) (dual of [4782993, 4782912, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(93, 24, F9, 2) (dual of [24, 21, 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(12) ⊂ Ce(9) [i] based on
- linear OA(981, 4782995, F9, 12) (dual of [4782995, 4782914, 13]-code), using Gilbert–Varšamov bound and bm = 981 > Vbs−1(k−1) = 6449 521079 776401 215371 956098 495556 207324 773567 379523 843934 556889 342143 427281 [i]
- linear OA(90, 2, F9, 0) (dual of [2, 2, 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(981, 4782993, F9, 13) (dual of [4782993, 4782912, 14]-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(983, 2391498, F9, 15, 13) (dual of [(2391498, 15), 35872387, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |