Information on Result #689029
Linear OA(937, 4782985, F9, 6) (dual of [4782985, 4782948, 7]-code), using construction X4 applied to Ce(5) ⊂ Ce(3) based on
- linear OA(936, 4782969, F9, 6) (dual of [4782969, 4782933, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(922, 4782969, F9, 4) (dual of [4782969, 4782947, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(938, 4782986, F9, 6) (dual of [4782986, 4782948, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(937, 4782985, F9, 2, 6) (dual of [(4782985, 2), 9565933, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(937, 4782985, F9, 3, 6) (dual of [(4782985, 3), 14348918, 7]-NRT-code) | [i] | ||
| 4 | Digital (31, 37, 4782985)-net over F9 | [i] | ||