Information on Result #1615128
Linear OOA(12874, 4754, F128, 4, 36) (dual of [(4754, 4), 18942, 37]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12874, 4754, F128, 3, 36) (dual of [(4754, 3), 14188, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12874, 5465, F128, 3, 36) (dual of [(5465, 3), 16321, 37]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12874, 16395, F128, 36) (dual of [16395, 16321, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(31) [i] based on
- linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(12863, 16384, F128, 32) (dual of [16384, 16321, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [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(35) ⊂ Ce(31) [i] based on
- OOA 3-folding [i] based on linear OA(12874, 16395, F128, 36) (dual of [16395, 16321, 37]-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(12874, 950, F128, 44, 36) (dual of [(950, 44), 41726, 37]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |