Information on Result #684687
Linear OA(7105, 117664, F7, 20) (dual of [117664, 117559, 21]-code), using construction XX applied to Ce(19) ⊂ Ce(17) ⊂ Ce(16) based on
- linear OA(7103, 117649, F7, 20) (dual of [117649, 117546, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(785, 117649, F7, 17) (dual of [117649, 117564, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(71, 14, F7, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), 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(7105, 96099, F7, 2, 20) (dual of [(96099, 2), 192093, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7105, 96099, F7, 3, 20) (dual of [(96099, 3), 288192, 21]-NRT-code) | [i] | ||
| 3 | Digital (85, 105, 96099)-net over F7 | [i] | ||
| 4 | Linear OOA(7105, 58832, F7, 2, 20) (dual of [(58832, 2), 117559, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(7105, 39221, F7, 3, 20) (dual of [(39221, 3), 117558, 21]-NRT-code) | [i] | ||