Information on Result #731029
Linear OA(744, 4814, F7, 11) (dual of [4814, 4770, 12]-code), using trace code based on linear OA(4922, 2407, F49, 11) (dual of [2407, 2385, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(4921, 2402, F49, 11) (dual of [2402, 2381, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(4917, 2402, F49, 9) (dual of [2402, 2385, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(491, 5, F49, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-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 OOA(744, 2407, F7, 2, 11) (dual of [(2407, 2), 4770, 12]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(744, 1604, F7, 3, 11) (dual of [(1604, 3), 4768, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(744, 962, F7, 11, 11) (dual of [(962, 11), 10538, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |