Information on Result #1614564
Linear OOA(12844, 8200, F128, 4, 20) (dual of [(8200, 4), 32756, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12844, 8200, F128, 2, 20) (dual of [(8200, 2), 16356, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12844, 16400, F128, 20) (dual of [16400, 16356, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12844, 16401, F128, 20) (dual of [16401, 16357, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1285, 17, F128, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(12844, 16401, F128, 20) (dual of [16401, 16357, 21]-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(12844, 2733, F128, 28, 20) (dual of [(2733, 28), 76480, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |