Information on Result #684495
Linear OA(7110, 5764831, F7, 16) (dual of [5764831, 5764721, 17]-code), using construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) based on
- linear OA(7105, 5764801, F7, 16) (dual of [5764801, 5764696, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(781, 5764801, F7, 12) (dual of [5764801, 5764720, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(773, 5764801, F7, 11) (dual of [5764801, 5764728, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(74, 29, F7, 3) (dual of [29, 25, 4]-code or 29-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(7110, 3828225, F7, 2, 16) (dual of [(3828225, 2), 7656340, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7110, 3828225, F7, 3, 16) (dual of [(3828225, 3), 11484565, 17]-NRT-code) | [i] | ||
| 3 | Digital (94, 110, 3828225)-net over F7 | [i] | ||
| 4 | Linear OOA(7110, 2882415, F7, 2, 16) (dual of [(2882415, 2), 5764720, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(7110, 1921610, F7, 3, 16) (dual of [(1921610, 3), 5764720, 17]-NRT-code) | [i] | ||