Information on Result #701297
Linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,27,34,41}, and minimum distance d ≥ |{−7,−6,…,23}|+1 = 32 (BCH-bound)
Mode: Constructive and linear.
This result is hidden, because other results with identical parameters exist.
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
- Contraction (with Narrow-Sense BCH-Code) (hidden) [i]
- Primitive Narrow-Sense BCH-Codes [i]
- Primitive BCH-Codes (hidden) [i]
- Primitive BCH-Codes (hidden) [i]
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(739, 48, F7, 30) (dual of [48, 9, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(739, 48, F7, 29) (dual of [48, 9, 30]-code) | [i] | ||
| 3 | Linear OA(739, 48, F7, 28) (dual of [48, 9, 29]-code) | [i] | ||
| 4 | Linear OA(784, 90, F7, 63) (dual of [90, 6, 64]-code) | [i] | Repeating Each Code Word | |
| 5 | Linear OA(783, 88, F7, 63) (dual of [88, 5, 64]-code) | [i] | ||
| 6 | Linear OA(796, 103, F7, 72) (dual of [103, 7, 73]-code) | [i] | Juxtaposition | |
| 7 | Linear OA(755, 78, F7, 30) (dual of [78, 23, 31]-code) | [i] | ✔ | Construction X with Cyclic Codes |
| 8 | Linear OA(755, 76, F7, 31) (dual of [76, 21, 32]-code) | [i] | ✔ | |
| 9 | Linear OA(754, 73, F7, 31) (dual of [73, 19, 32]-code) | [i] | ✔ | |
| 10 | Linear OA(749, 68, F7, 28) (dual of [68, 19, 29]-code) | [i] | ✔ | |
| 11 | Linear OA(749, 66, F7, 29) (dual of [66, 17, 30]-code) | [i] | ✔ | |
| 12 | Linear OA(752, 73, F7, 29) (dual of [73, 21, 30]-code) | [i] | ✔ | Construction XX with Cyclic Codes |
| 13 | Linear OA(750, 71, F7, 28) (dual of [71, 21, 29]-code) | [i] | ✔ | |
| 14 | Linear OA(745, 64, F7, 27) (dual of [64, 19, 28]-code) | [i] | ✔ | |
| 15 | Linear OA(747, 64, F7, 28) (dual of [64, 17, 29]-code) | [i] | ✔ | |
| 16 | Linear OA(757, 73, F7, 35) (dual of [73, 16, 36]-code) | [i] | ✔ | |
| 17 | Linear OOA(739, 24, F7, 2, 31) (dual of [(24, 2), 9, 32]-NRT-code) | [i] | OOA Folding | |
| 18 | Linear OOA(739, 16, F7, 3, 31) (dual of [(16, 3), 9, 32]-NRT-code) | [i] | ||