Information on Result #684705
Linear OA(742, 117673, F7, 8) (dual of [117673, 117631, 9]-code), using construction XX applied to Ce(7) ⊂ Ce(3) ⊂ Ce(2) based on
- linear OA(737, 117649, F7, 8) (dual of [117649, 117612, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(719, 117649, F7, 4) (dual of [117649, 117630, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(713, 117649, F7, 3) (dual of [117649, 117636, 4]-code or 117649-cap in PG(12,7)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(74, 23, F7, 3) (dual of [23, 19, 4]-code or 23-cap in PG(3,7)), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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(742, 117673, F7, 2, 8) (dual of [(117673, 2), 235304, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(742, 117673, F7, 3, 8) (dual of [(117673, 3), 352977, 9]-NRT-code) | [i] | ||
| 3 | Digital (34, 42, 117673)-net over F7 | [i] | ||
| 4 | Linear OOA(742, 58836, F7, 2, 8) (dual of [(58836, 2), 117630, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(742, 39224, F7, 3, 8) (dual of [(39224, 3), 117630, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(742, 29418, F7, 8, 8) (dual of [(29418, 8), 235302, 9]-NRT-code) | [i] | OA Folding and Stacking | |