Information on Result #684704
Linear OA(739, 117658, F7, 8) (dual of [117658, 117619, 9]-code), using construction XX applied to Ce(7) ⊂ Ce(5) ⊂ Ce(4) 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(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(725, 117649, F7, 5) (dual of [117649, 117624, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(71, 8, F7, 1) (dual of [8, 7, 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(739, 112291, F7, 2, 8) (dual of [(112291, 2), 224543, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(739, 112291, F7, 3, 8) (dual of [(112291, 3), 336834, 9]-NRT-code) | [i] | ||
| 3 | Digital (31, 39, 112291)-net over F7 | [i] | ||
| 4 | Linear OOA(739, 58829, F7, 2, 8) (dual of [(58829, 2), 117619, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(739, 39219, F7, 3, 8) (dual of [(39219, 3), 117618, 9]-NRT-code) | [i] | ||