Information on Result #1014392
Linear OOA(8103, 5608788, F8, 3, 11) (dual of [(5608788, 3), 16826261, 12]-NRT-code), using (u, u+v)-construction based on
- linear OOA(821, 16386, F8, 3, 5) (dual of [(16386, 3), 49137, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(821, 32773, F8, 5) (dual of [32773, 32752, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(821, 32768, F8, 5) (dual of [32768, 32747, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(816, 32768, F8, 4) (dual of [32768, 32752, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(821, 32773, F8, 5) (dual of [32773, 32752, 6]-code), using
- linear OOA(882, 5592402, F8, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
- trace code [i] based on linear OOA(6441, 2796201, F64, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- trace code [i] based on linear OOA(6441, 2796201, F64, 3, 11) (dual of [(2796201, 3), 8388562, 12]-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(8103, 2804393, F8, 15, 11) (dual of [(2804393, 15), 42065792, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |