Information on Result #1022589
Linear OOA(8177, 5858126, F81, 3, 12) (dual of [(5858126, 3), 17574301, 13]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(8111, 265724, F81, 3, 4) (dual of [(265724, 3), 797161, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(8111, 531448, F81, 4) (dual of [531448, 531437, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(814, 531441, F81, 2) (dual of [531441, 531437, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(8111, 531448, F81, 4) (dual of [531448, 531437, 5]-code), using
- linear OOA(8121, 2796201, F81, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8121, large, F81, 6) (dual of [large, large−21, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(8121, large, F81, 6) (dual of [large, large−21, 7]-code), using
- linear OOA(8145, 2796201, F81, 3, 12) (dual of [(2796201, 3), 8388558, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-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(8177, 2929062, F81, 15, 12) (dual of [(2929062, 15), 43935853, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |