Information on Result #619766
Linear OA(2567, 257, F256, 7) (dual of [257, 250, 8]-code or 257-arc in PG(6,256)), using the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound)
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
- Extended Reed–Solomon Code [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
- Algebraic-Geometric Codes Defined Using a Non-Rational Place [i]
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(428, 1028, F4, 7) (dual of [1028, 1000, 8]-code) | [i] | Trace Code | |
| 2 | Linear OA(1614, 514, F16, 7) (dual of [514, 500, 8]-code) | [i] | ||
| 3 | OA(3212, 257, S32, 7) | [i] | Discarding Parts of the Base for OAs | |
| 4 | OA(6410, 257, S64, 7) | [i] | ||
| 5 | OA(1288, 257, S128, 7) | [i] | ||
| 6 | Linear OA(25622, 514, F256, 15) (dual of [514, 492, 16]-code) | [i] | (u, u+v)-Construction | |
| 7 | Linear OA(25623, 517, F256, 15) (dual of [517, 494, 16]-code) | [i] | ||
| 8 | Linear OA(25636, 65794, F256, 15) (dual of [65794, 65758, 16]-code) | [i] | ||
| 9 | Linear OA(25621, 514, F256, 14) (dual of [514, 493, 15]-code) | [i] | ||
| 10 | Linear OA(25622, 517, F256, 14) (dual of [517, 495, 15]-code) | [i] | ||
| 11 | Linear OA(25634, 65793, F256, 14) (dual of [65793, 65759, 15]-code) | [i] | ||
| 12 | Linear OA(25610, 514, F256, 7) (dual of [514, 504, 8]-code) | [i] | ||
| 13 | Linear OA(25636, 65795, F256, 15) (dual of [65795, 65759, 16]-code) | [i] | ||
| 14 | Linear OA(25637, 65799, F256, 15) (dual of [65799, 65762, 16]-code) | [i] | ||
| 15 | Linear OA(25634, 65795, F256, 14) (dual of [65795, 65761, 15]-code) | [i] | ||
| 16 | Linear OA(25623, 546, F256, 15) (dual of [546, 523, 16]-code) | [i] | ||
| 17 | Linear OA(25622, 546, F256, 14) (dual of [546, 524, 15]-code) | [i] | ||
| 18 | Linear OA(25616, 65792, F256, 7) (dual of [65792, 65776, 8]-code) | [i] | Generalized (u, u+v)-Construction | |
| 19 | Linear OA(25663, 66051, F256, 23) (dual of [66051, 65988, 24]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 20 | Linear OA(25664, 66054, F256, 23) (dual of [66054, 65990, 24]-code) | [i] | ||
| 21 | Linear OA(25661, 66050, F256, 22) (dual of [66050, 65989, 23]-code) | [i] | ||
| 22 | Linear OA(25662, 66053, F256, 22) (dual of [66053, 65991, 23]-code) | [i] | ||
| 23 | Linear OA(25658, 66051, F256, 21) (dual of [66051, 65993, 22]-code) | [i] | ||
| 24 | Linear OA(25659, 66054, F256, 21) (dual of [66054, 65995, 22]-code) | [i] | ||
| 25 | Linear OA(25641, 66051, F256, 15) (dual of [66051, 66010, 16]-code) | [i] | ||
| 26 | Linear OA(25638, 66050, F256, 14) (dual of [66050, 66012, 15]-code) | [i] | ||
| 27 | Linear OA(2569, 260, F256, 7) (dual of [260, 251, 8]-code) | [i] | ✔ | Construction X with Cyclic Codes |