Information on Result #689073
Linear OA(998, 4783010, F9, 15) (dual of [4783010, 4782912, 16]-code), using construction X applied to Ce(14) ⊂ Ce(9) based on
- linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(96, 41, F9, 4) (dual of [41, 35, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-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(999, 4783011, F9, 15) (dual of [4783011, 4782912, 16]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(9100, 4783012, F9, 15) (dual of [4783012, 4782912, 16]-code) | [i] | ||
| 3 | Linear OA(9101, 4783013, F9, 15) (dual of [4783013, 4782912, 16]-code) | [i] | ||
| 4 | Linear OA(9102, 4783014, F9, 15) (dual of [4783014, 4782912, 16]-code) | [i] | ||
| 5 | Linear OOA(998, 4783010, F9, 2, 15) (dual of [(4783010, 2), 9565922, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(998, 4783010, F9, 3, 15) (dual of [(4783010, 3), 14348932, 16]-NRT-code) | [i] | ||
| 7 | Digital (83, 98, 4783010)-net over F9 | [i] | ||
| 8 | Linear OOA(998, 2391505, F9, 2, 15) (dual of [(2391505, 2), 4782912, 16]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(998, 1594336, F9, 3, 15) (dual of [(1594336, 3), 4782910, 16]-NRT-code) | [i] | ||
| 10 | Linear OOA(998, 683287, F9, 15, 15) (dual of [(683287, 15), 10249207, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |