Information on Result #698752

Linear OA(647, 4098, F64, 4) (dual of [4098, 4091, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
  1. linear OA(647, 4096, F64, 4) (dual of [4096, 4089, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
  2. linear OA(645, 4096, F64, 3) (dual of [4096, 4091, 4]-code or 4096-cap in PG(4,64)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
  3. linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-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:

ResultThis
result
only		Method
1Linear OA(814, 8196, F8, 4) (dual of [8196, 8182, 5]-code) [i]Trace Code
2OA(329, 4098, S32, 4) [i]Discarding Parts of the Base for OAs
3Linear OA(6432, 266245, F64, 9) (dual of [266245, 266213, 10]-code) [i](u, u+v)-Construction
4Linear OA(6412, 262272, F64, 4) (dual of [262272, 262260, 5]-code) [i]Generalized (u, u+v)-Construction
5Linear OOA(647, 4098, F64, 2, 4) (dual of [(4098, 2), 8189, 5]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
6Linear OOA(647, 4098, F64, 3, 4) (dual of [(4098, 3), 12287, 5]-NRT-code) [i]
7Linear OA(648, 4226, F64, 4) (dual of [4226, 4218, 5]-code) [i]VarÅ¡amov–Edel Lengthening
8Linear OOA(647, 2049, F64, 2, 4) (dual of [(2049, 2), 4091, 5]-NRT-code) [i]OOA Folding
9Linear OOA(647, 2049, F64, 3, 4) (dual of [(2049, 3), 6140, 5]-NRT-code) [i]OA Folding and Stacking