Information on Result #1022726
Linear OOA(12877, 5600595, F128, 3, 13) (dual of [(5600595, 3), 16801708, 14]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(1287, 8193, F128, 3, 4) (dual of [(8193, 3), 24572, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(1287, 16386, F128, 4) (dual of [16386, 16379, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(1287, 16384, F128, 4) (dual of [16384, 16377, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1285, 16384, F128, 3) (dual of [16384, 16379, 4]-code or 16384-cap in PG(4,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- OA 2-folding and stacking [i] based on linear OA(1287, 16386, F128, 4) (dual of [16386, 16379, 5]-code), using
- linear OOA(12821, 2796201, F128, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12821, large, F128, 6) (dual of [large, large−21, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OOA 3-folding [i] based on linear OA(12821, large, F128, 6) (dual of [large, large−21, 7]-code), using
- linear OOA(12849, 2796201, F128, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12849, large, F128, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(12849, large, F128, 13) (dual of [large, large−49, 14]-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(12877, 2800297, F128, 15, 13) (dual of [(2800297, 15), 42004378, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |