Information on Result #735082
Linear OA(6437, 4228, F64, 14) (dual of [4228, 4191, 15]-code), using (u, u+v)-construction based on
- linear OA(6410, 130, F64, 7) (dual of [130, 120, 8]-code), using
- (u, u+v)-construction [i] based on
- linear OA(643, 65, F64, 3) (dual of [65, 62, 4]-code or 65-arc in PG(2,64) or 65-cap in PG(2,64)), using
- extended Reed–Solomon code RSe(62,64) [i]
- linear OA(647, 65, F64, 7) (dual of [65, 58, 8]-code or 65-arc in PG(6,64)), using
- extended Reed–Solomon code RSe(58,64) [i]
- the expurgated narrow-sense BCH-code C(I) with length 65 | 642−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(643, 65, F64, 3) (dual of [65, 62, 4]-code or 65-arc in PG(2,64) or 65-cap in PG(2,64)), using
- (u, u+v)-construction [i] based on
- linear OA(6427, 4098, F64, 14) (dual of [4098, 4071, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(6425, 4096, F64, 13) (dual of [4096, 4071, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
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 OOA(6437, 2114, F64, 2, 14) (dual of [(2114, 2), 4191, 15]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(6437, 1409, F64, 3, 14) (dual of [(1409, 3), 4190, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(6437, 604, F64, 14, 14) (dual of [(604, 14), 8419, 15]-NRT-code) | [i] | OA Folding and Stacking | |