Information on Result #1614735
Linear OOA(12854, 2097284, F128, 4, 16) (dual of [(2097284, 4), 8389082, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(12854, 2097284, F128, 16) (dual of [2097284, 2097230, 17]-code), using
- (u, u+v)-construction [i] based on
- linear OA(1288, 129, F128, 8) (dual of [129, 121, 9]-code or 129-arc in PG(7,128)), using
- extended Reed–Solomon code RSe(121,128) [i]
- linear OA(12846, 2097155, F128, 16) (dual of [2097155, 2097109, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12843, 2097152, F128, 15) (dual of [2097152, 2097109, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(1288, 129, F128, 8) (dual of [129, 121, 9]-code or 129-arc in PG(7,128)), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(12854, 1048641, F128, 20, 16) (dual of [(1048641, 20), 20972766, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |