Information on Result #906955
Linear OOA(4937, large, F49, 2, 7), using generalized (u, u+v)-construction based on
- linear OOA(495, 2882402, F49, 2, 2) (dual of [(2882402, 2), 5764799, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(495, 5884901, F49, 2, 2) (dual of [(5884901, 2), 11769797, 3]-NRT-code), using
- appending kth column [i] based on linear OA(495, 5884901, F49, 2) (dual of [5884901, 5884896, 3]-code), using
- Hamming code H(5,49) [i]
- appending kth column [i] based on linear OA(495, 5884901, F49, 2) (dual of [5884901, 5884896, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(495, 5884901, F49, 2, 2) (dual of [(5884901, 2), 11769797, 3]-NRT-code), using
- linear OOA(497, 2882402, F49, 2, 3) (dual of [(2882402, 2), 5764797, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(497, 5769603, F49, 2, 3) (dual of [(5769603, 2), 11539199, 4]-NRT-code), using
- linear OOA(4925, 2882402, F49, 2, 7) (dual of [(2882402, 2), 5764779, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4925, 5764804, F49, 7) (dual of [5764804, 5764779, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 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
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(4925, 5764805, F49, 7) (dual of [5764805, 5764780, 8]-code), using
- OOA 2-folding [i] based on linear OA(4925, 5764804, F49, 7) (dual of [5764804, 5764779, 8]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m 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(4937, large, F49, 2, 6) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(4937, large, F49, 2, 5) | [i] | ||
| 3 | Linear OOA(4937, large, F49, 2, 4) | [i] | ||
| 4 | Linear OOA(4937, large, F49, 2, 3) | [i] | ||
| 5 | Linear OOA(4941, large, F49, 2, 7) | [i] | NRT-Code Embedding in Larger Space | |
| 6 | Linear OOA(4943, large, F49, 2, 7) | [i] | ||
| 7 | Linear OOA(4945, large, F49, 2, 7) | [i] | ||
| 8 | Linear OOA(4937, 4194301, F49, 3, 7) (dual of [(4194301, 3), 12582866, 8]-NRT-code) | [i] | OOA Folding | |