Information on Result #1302007
Linear OA(744, 16823, F7, 10) (dual of [16823, 16779, 11]-code), using construction X with Varšamov bound based on
- linear OA(742, 16819, F7, 10) (dual of [16819, 16777, 11]-code), using
- construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(741, 16807, F7, 10) (dual of [16807, 16766, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(731, 16807, F7, 8) (dual of [16807, 16776, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(711, 12, F7, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,7)), using
- dual of repetition code with length 12 [i]
- linear OA(71, 12, F7, 1) (dual of [12, 11, 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
- construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(742, 16821, F7, 9) (dual of [16821, 16779, 10]-code), using Gilbert–Varšamov bound and bm = 742 > Vbs−1(k−1) = 266445 740947 936920 661381 146311 292385 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 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
Mode: 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(744, 16823, F7, 2, 10) (dual of [(16823, 2), 33602, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(744, 16823, F7, 3, 10) (dual of [(16823, 3), 50425, 11]-NRT-code) | [i] | ||
| 3 | Digital (34, 44, 16823)-net over F7 | [i] | ||
| 4 | Linear OOA(744, 8411, F7, 2, 10) (dual of [(8411, 2), 16778, 11]-NRT-code) | [i] | OOA Folding | |