Information on Result #689103
Linear OA(9139, 4782996, F9, 22) (dual of [4782996, 4782857, 23]-code), using construction XX applied to Ce(21) ⊂ Ce(18) ⊂ Ce(16) based on
- linear OA(9134, 4782969, F9, 22) (dual of [4782969, 4782835, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(93, 25, F9, 2) (dual of [25, 22, 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
- linear OA(91, 2, F9, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(9139, 3985550, F9, 2, 22) (dual of [(3985550, 2), 7970961, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(9139, 3985550, F9, 3, 22) (dual of [(3985550, 3), 11956511, 23]-NRT-code) | [i] | ||
| 3 | Digital (117, 139, 3985550)-net over F9 | [i] | ||
| 4 | Linear OOA(9139, 2391498, F9, 2, 22) (dual of [(2391498, 2), 4782857, 23]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(9139, 1594332, F9, 3, 22) (dual of [(1594332, 3), 4782857, 23]-NRT-code) | [i] | ||