Information on Result #698605
Linear OA(6430, 4102, F64, 15) (dual of [4102, 4072, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,6]) based on
- linear OA(6429, 4097, F64, 15) (dual of [4097, 4068, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(6425, 4097, F64, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(860, 8204, F8, 15) (dual of [8204, 8144, 16]-code) | [i] | Trace Code | |
| 2 | OA(3236, 4102, S32, 15) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(6438, 4182, F64, 15) (dual of [4182, 4144, 16]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(6433, 4112, F64, 15) (dual of [4112, 4079, 16]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(6434, 4142, F64, 15) (dual of [4142, 4108, 16]-code) | [i] | ||
| 6 | Linear OA(6435, 4262, F64, 15) (dual of [4262, 4227, 16]-code) | [i] | ||
| 7 | Linear OA(6436, 4682, F64, 15) (dual of [4682, 4646, 16]-code) | [i] | ||
| 8 | Linear OOA(6430, 2051, F64, 2, 15) (dual of [(2051, 2), 4072, 16]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(6430, 1367, F64, 3, 15) (dual of [(1367, 3), 4071, 16]-NRT-code) | [i] | ||