Information on Result #896333
Linear OOA(791, 5767214, F7, 2, 10) (dual of [(5767214, 2), 11534337, 11]-NRT-code), using (u, u+v)-construction based on
- linear OOA(717, 2410, F7, 2, 5) (dual of [(2410, 2), 4803, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(73, 57, F7, 2, 2) (dual of [(57, 2), 111, 3]-NRT-code), using
- appending kth column [i] based on linear OA(73, 57, F7, 2) (dual of [57, 54, 3]-code), using
- Hamming code H(3,7) [i]
- appending kth column [i] based on linear OA(73, 57, F7, 2) (dual of [57, 54, 3]-code), using
- linear OOA(714, 2353, F7, 2, 5) (dual of [(2353, 2), 4692, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(714, 4706, F7, 5) (dual of [4706, 4692, 6]-code), using
- trace code [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
- OOA 2-folding [i] based on linear OA(714, 4706, F7, 5) (dual of [4706, 4692, 6]-code), using
- linear OOA(73, 57, F7, 2, 2) (dual of [(57, 2), 111, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(774, 5764804, F7, 2, 10) (dual of [(5764804, 2), 11529534, 11]-NRT-code), using
- trace code [i] based on linear OOA(4937, 2882402, F49, 2, 10) (dual of [(2882402, 2), 5764767, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4937, 5764804, F49, 10) (dual of [5764804, 5764767, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4937, 5764805, F49, 10) (dual of [5764805, 5764768, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(4937, 5764801, F49, 10) (dual of [5764801, 5764764, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(4937, 5764805, F49, 10) (dual of [5764805, 5764768, 11]-code), using
- OOA 2-folding [i] based on linear OA(4937, 5764804, F49, 10) (dual of [5764804, 5764767, 11]-code), using
- trace code [i] based on linear OOA(4937, 2882402, F49, 2, 10) (dual of [(2882402, 2), 5764767, 11]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, 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(791, 2883607, F7, 3, 10) (dual of [(2883607, 3), 8650730, 11]-NRT-code) | [i] | OOA Folding | |