Information on Result #905029
Linear OOA(12878, 4202497, F128, 2, 16) (dual of [(4202497, 2), 8404916, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12817, 8196, F128, 2, 8) (dual of [(8196, 2), 16375, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12817, 16392, F128, 8) (dual of [16392, 16375, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- linear OA(12815, 16384, F128, 8) (dual of [16384, 16369, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1289, 16384, F128, 5) (dual of [16384, 16375, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(7) ⊂ Ce(4) [i] based on
- OOA 2-folding [i] based on linear OA(12817, 16392, F128, 8) (dual of [16392, 16375, 9]-code), using
- linear OOA(12861, 4194301, F128, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12861, 8388602, F128, 16) (dual of [8388602, 8388541, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(12861, large, F128, 16) (dual of [large, large−61, 17]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(12861, large, F128, 16) (dual of [large, large−61, 17]-code), using
- OOA 2-folding [i] based on linear OA(12861, 8388602, F128, 16) (dual of [8388602, 8388541, 17]-code), using
Mode: Constructive and 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(12878, 2101248, F128, 4, 16) (dual of [(2101248, 4), 8404914, 17]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(12878, 1050624, F128, 18, 16) (dual of [(1050624, 18), 18911154, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |