Information on Result #1022684
Linear OOA(12862, 6291459, F128, 3, 11) (dual of [(6291459, 3), 18874315, 12]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 3, 1) for arbitrarily large s, using
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
- linear OOA(1284, 699051, F128, 3, 2) (dual of [(699051, 3), 2097149, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 3, 2) (dual of [(2113665, 3), 6340991, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- Hamming code H(4,128) [i]
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 3, 2) (dual of [(2113665, 3), 6340991, 3]-NRT-code), using
- linear OOA(1284, 699051, F128, 3, 2) (dual of [(699051, 3), 2097149, 3]-NRT-code) (see above)
- linear OOA(1286, 699051, F128, 3, 3) (dual of [(699051, 3), 2097147, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1286, 2130049, F128, 3, 3) (dual of [(2130049, 3), 6390141, 4]-NRT-code), using
- linear OOA(12813, 699051, F128, 3, 5) (dual of [(699051, 3), 2097140, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12813, 1048577, F128, 3, 5) (dual of [(1048577, 3), 3145718, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(12813, 2097155, F128, 5) (dual of [2097155, 2097142, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(12813, 2097152, F128, 5) (dual of [2097152, 2097139, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 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(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(12813, 2097155, F128, 5) (dual of [2097155, 2097142, 6]-code), using
- discarding factors / shortening the dual code based on linear OOA(12813, 1048577, F128, 3, 5) (dual of [(1048577, 3), 3145718, 6]-NRT-code), using
- linear OOA(12831, 699051, F128, 3, 11) (dual of [(699051, 3), 2097122, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12831, 2097153, F128, 11) (dual of [2097153, 2097122, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(12831, 2097153, F128, 11) (dual of [2097153, 2097122, 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(12862, 3145729, F128, 15, 11) (dual of [(3145729, 15), 47185873, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |