Information on Result #1449967
Linear OOA(982, 4782995, F9, 2, 13) (dual of [(4782995, 2), 9565908, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(982, 4782995, F9, 13) (dual of [4782995, 4782913, 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, 4782994, F9, 12) (dual of [4782994, 4782913, 13]-code), using Gilbert–Varšamov bound and bm = 981 > Vbs−1(k−1) = 6449 506247 073281 903877 424413 243569 457554 605908 861669 691546 529797 412205 690505 [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(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(982, 2391497, F9, 3, 13) (dual of [(2391497, 3), 7174409, 14]-NRT-code) | [i] | OOA Folding | |