Information on Result #688958
Linear OA(944, 4782986, F9, 7) (dual of [4782986, 4782942, 8]-code), using construction X4 applied to C([0,3]) ⊂ C([0,2]) based on
- linear OA(943, 4782970, F9, 7) (dual of [4782970, 4782927, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(929, 4782970, F9, 5) (dual of [4782970, 4782941, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [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 OA(945, 4782987, F9, 7) (dual of [4782987, 4782942, 8]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(944, 4782986, F9, 2, 7) (dual of [(4782986, 2), 9565928, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(944, 4782986, F9, 3, 7) (dual of [(4782986, 3), 14348914, 8]-NRT-code) | [i] | ||
| 4 | Digital (37, 44, 4782986)-net over F9 | [i] | ||
| 5 | Linear OOA(944, 2391493, F9, 2, 7) (dual of [(2391493, 2), 4782942, 8]-NRT-code) | [i] | OOA Folding | |