Information on Result #2283665
Linear OA(973, 4782986, F9, 12) (dual of [4782986, 4782913, 13]-code), using 1 times code embedding in larger space based on linear OA(972, 4782985, F9, 12) (dual of [4782985, 4782913, 13]-code), using
- construction X4 applied to Ce(11) ⊂ Ce(9) [i] based on
- 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(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(915, 16, F9, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,9)), using
- dual of repetition code with length 16 [i]
- linear OA(91, 16, F9, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-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(973, 4201766, F9, 2, 12) (dual of [(4201766, 2), 8403459, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(973, 4201766, F9, 3, 12) (dual of [(4201766, 3), 12605225, 13]-NRT-code) | [i] | ||
| 3 | Digital (61, 73, 4201766)-net over F9 | [i] | ||
| 4 | Linear OA(974, 4782988, F9, 12) (dual of [4782988, 4782914, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(973, 2391493, F9, 2, 12) (dual of [(2391493, 2), 4782913, 13]-NRT-code) | [i] | OOA Folding | |