Information on Result #689045
Linear OA(981, 4782993, F9, 13) (dual of [4782993, 4782912, 14]-code), using construction X applied to Ce(12) ⊂ Ce(9) 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
Mode: Constructive and 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 OA(982, 4782994, F9, 13) (dual of [4782994, 4782912, 14]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(981, 4782993, F9, 2, 13) (dual of [(4782993, 2), 9565905, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(981, 4782993, F9, 3, 13) (dual of [(4782993, 3), 14348898, 14]-NRT-code) | [i] | ||
| 4 | Digital (68, 81, 4782993)-net over F9 | [i] | ||
| 5 | Linear OA(982, 4782995, F9, 13) (dual of [4782995, 4782913, 14]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OA(983, 4782997, F9, 13) (dual of [4782997, 4782914, 14]-code) | [i] | ||
| 7 | Linear OOA(981, 2391496, F9, 2, 13) (dual of [(2391496, 2), 4782911, 14]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(981, 1594331, F9, 3, 13) (dual of [(1594331, 3), 4782912, 14]-NRT-code) | [i] | ||
| 9 | Linear OOA(981, 797165, F9, 13, 13) (dual of [(797165, 13), 10363064, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |