Information on Result #1014023
Linear OOA(787, 5619, F7, 3, 18) (dual of [(5619, 3), 16770, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(710, 13, F7, 3, 9) (dual of [(13, 3), 29, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 10, 13)-net over F7, using
- 3 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- extracting embedded OOA [i] based on digital (1, 10, 13)-net over F7, using
- linear OOA(777, 5606, F7, 3, 18) (dual of [(5606, 3), 16741, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(777, 16818, F7, 18) (dual of [16818, 16741, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(766, 16807, F7, 16) (dual of [16807, 16741, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- OOA 3-folding [i] based on linear OA(777, 16818, F7, 18) (dual of [16818, 16741, 19]-code), using
Mode: Constructive and 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(788, 5619, F7, 3, 18) (dual of [(5619, 3), 16769, 19]-NRT-code) | [i] | OOA Duplication | |