Information on Result #689088
Linear OA(9133, 4783031, F9, 20) (dual of [4783031, 4782898, 21]-code), using construction X applied to Ce(19) ⊂ Ce(11) based on
- linear OA(9120, 4782969, F9, 20) (dual of [4782969, 4782849, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(913, 62, F9, 7) (dual of [62, 49, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(913, 80, F9, 7) (dual of [80, 67, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(913, 80, F9, 7) (dual of [80, 67, 8]-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 OOA(9133, 4783031, F9, 2, 20) (dual of [(4783031, 2), 9565929, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9133, 4783031, F9, 3, 20) (dual of [(4783031, 3), 14348960, 21]-NRT-code) | [i] | ||
| 3 | Digital (113, 133, 4783031)-net over F9 | [i] | ||