Information on Result #684702
Linear OA(745, 117658, F7, 9) (dual of [117658, 117613, 10]-code), using construction XX applied to Ce(8) ⊂ Ce(7) ⊂ Ce(5) based on
- linear OA(743, 117649, F7, 9) (dual of [117649, 117606, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 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(731, 117649, F7, 6) (dual of [117649, 117618, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(70, 7, F7, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(71, 2, F7, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(745, 115558, F7, 2, 9) (dual of [(115558, 2), 231071, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(745, 115558, F7, 3, 9) (dual of [(115558, 3), 346629, 10]-NRT-code) | [i] | ||
| 3 | Digital (36, 45, 115558)-net over F7 | [i] | ||
| 4 | Linear OOA(745, 58829, F7, 2, 9) (dual of [(58829, 2), 117613, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(745, 39219, F7, 3, 9) (dual of [(39219, 3), 117612, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(745, 29414, F7, 9, 9) (dual of [(29414, 9), 264681, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |