Information on Result #688961
Linear OA(930, 4782986, F9, 5) (dual of [4782986, 4782956, 6]-code), using construction X4 applied to C([0,2]) ⊂ C([0,1]) based on
- 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, 4782970, F9, 3) (dual of [4782970, 4782955, 4]-code or 4782970-cap in PG(14,9)), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (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(931, 4782987, F9, 5) (dual of [4782987, 4782956, 6]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(930, 4782986, F9, 2, 5) (dual of [(4782986, 2), 9565942, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(930, 4782986, F9, 3, 5) (dual of [(4782986, 3), 14348928, 6]-NRT-code) | [i] | ||
| 4 | Digital (25, 30, 4782986)-net over F9 | [i] | ||
| 5 | Linear OOA(930, 2391493, F9, 2, 5) (dual of [(2391493, 2), 4782956, 6]-NRT-code) | [i] | OOA Folding | |