Information on Result #1014646
Linear OOA(8168, 5767169, F8, 3, 16) (dual of [(5767169, 3), 17301339, 17]-NRT-code), using (u, u+v)-construction based on
- linear OOA(846, 174767, F8, 3, 8) (dual of [(174767, 3), 524255, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(846, 524301, F8, 8) (dual of [524301, 524255, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(846, 524302, F8, 8) (dual of [524302, 524256, 9]-code), using
- trace code [i] based on linear OA(6423, 262151, F64, 8) (dual of [262151, 262128, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(6422, 262144, F64, 8) (dual of [262144, 262122, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(6423, 262151, F64, 8) (dual of [262151, 262128, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(846, 524302, F8, 8) (dual of [524302, 524256, 9]-code), using
- OOA 3-folding [i] based on linear OA(846, 524301, F8, 8) (dual of [524301, 524255, 9]-code), using
- linear OOA(8122, 5592402, F8, 3, 16) (dual of [(5592402, 3), 16777084, 17]-NRT-code), using
- trace code [i] based on linear OOA(6461, 2796201, F64, 3, 16) (dual of [(2796201, 3), 8388542, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 3-folding [i] based on linear OA(6461, large, F64, 16) (dual of [large, large−61, 17]-code), using
- trace code [i] based on linear OOA(6461, 2796201, F64, 3, 16) (dual of [(2796201, 3), 8388542, 17]-NRT-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(8169, 5767169, F8, 3, 16) (dual of [(5767169, 3), 17301338, 17]-NRT-code) | [i] | OOA Duplication | |