Information on Result #1614443
Linear OOA(12834, 6858, F128, 4, 16) (dual of [(6858, 4), 27398, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12834, 6858, F128, 2, 16) (dual of [(6858, 2), 13682, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12834, 8197, F128, 2, 16) (dual of [(8197, 2), 16360, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12834, 16394, F128, 16) (dual of [16394, 16360, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(12834, 16395, F128, 16) (dual of [16395, 16361, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(12834, 16395, F128, 16) (dual of [16395, 16361, 17]-code), using
- OOA 2-folding [i] based on linear OA(12834, 16394, F128, 16) (dual of [16394, 16360, 17]-code), using
Mode: 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(12834, 3428, F128, 20, 16) (dual of [(3428, 20), 68526, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |