Information on Result #1082464
Linear OOA(8158, 2099339, F81, 4, 12) (dual of [(2099339, 4), 8397298, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8113, 2189, F81, 4, 6) (dual of [(2189, 4), 8743, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(8113, 6567, F81, 6) (dual of [6567, 6554, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(8113, 6569, F81, 6) (dual of [6569, 6556, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(815, 6561, F81, 3) (dual of [6561, 6556, 4]-code or 6561-cap in PG(4,81)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(8113, 6569, F81, 6) (dual of [6569, 6556, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(8113, 6567, F81, 6) (dual of [6567, 6554, 7]-code), using
- linear OOA(8145, 2097150, F81, 4, 12) (dual of [(2097150, 4), 8388555, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8145, 8388600, F81, 12) (dual of [8388600, 8388555, 13]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- OOA 4-folding [i] based on linear OA(8145, 8388600, F81, 12) (dual of [8388600, 8388555, 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(8179, 4198678, F81, 4, 12) (dual of [(4198678, 4), 16794633, 13]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |