Information on Result #731028
Linear OA(742, 4806, F7, 11) (dual of [4806, 4764, 12]-code), using trace code based on linear OA(4921, 2403, F49, 11) (dual of [2403, 2382, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(4921, 2401, F49, 11) (dual of [2401, 2380, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(4919, 2401, F49, 10) (dual of [2401, 2382, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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 OA(743, 4807, F7, 11) (dual of [4807, 4764, 12]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(742, 4806, F7, 2, 11) (dual of [(4806, 2), 9570, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(742, 4806, F7, 3, 11) (dual of [(4806, 3), 14376, 12]-NRT-code) | [i] | ||
| 4 | Digital (31, 42, 4806)-net over F7 | [i] | ||
| 5 | Linear OA(743, 4815, F7, 11) (dual of [4815, 4772, 12]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(744, 4870, F7, 11) (dual of [4870, 4826, 12]-code) | [i] | ||
| 7 | Linear OA(743, 4808, F7, 11) (dual of [4808, 4765, 12]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OOA(742, 2403, F7, 2, 11) (dual of [(2403, 2), 4764, 12]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(742, 1602, F7, 3, 11) (dual of [(1602, 3), 4764, 12]-NRT-code) | [i] | ||
| 10 | Linear OOA(742, 961, F7, 11, 11) (dual of [(961, 11), 10529, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |