Information on Result #1083010
Linear OOA(12855, 3145730, F128, 4, 11) (dual of [(3145730, 4), 12582865, 12]-NRT-code), using (u, u+v)-construction based on
- linear OOA(12814, 1048580, F128, 4, 5) (dual of [(1048580, 4), 4194306, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(12814, 2097161, F128, 5) (dual of [2097161, 2097147, 6]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(12813, 2097153, F128, 5) (dual of [2097153, 2097140, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(1287, 2097153, F128, 3) (dual of [2097153, 2097146, 4]-code or 2097153-cap in PG(6,128)), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(1287, 8, F128, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,128)), using
- dual of repetition code with length 8 [i]
- linear OA(1281, 8, F128, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), using
- Reed–Solomon code RS(127,128) [i]
- discarding factors / shortening the dual code based on linear OA(1281, 128, F128, 1) (dual of [128, 127, 2]-code), using
- construction X4 applied to C([0,2]) ⊂ C([0,1]) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(12814, 2097161, F128, 5) (dual of [2097161, 2097147, 6]-code), using
- linear OOA(12841, 2097150, F128, 4, 11) (dual of [(2097150, 4), 8388559, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12841, 8388600, F128, 11) (dual of [8388600, 8388559, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(12841, large, F128, 11) (dual of [large, large−41, 12]-code), using
- OOA 4-folding [i] based on linear OA(12841, 8388600, F128, 11) (dual of [8388600, 8388559, 12]-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(12872, 6291460, F128, 4, 11) (dual of [(6291460, 4), 25165768, 12]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |