Information on Result #1653611
Linear OOA(2251, 1678068, F2, 5, 19) (dual of [(1678068, 5), 8390089, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(243, 348, F2, 5, 9) (dual of [(348, 5), 1697, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(243, 348, F2, 3, 9) (dual of [(348, 3), 1001, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(243, 1044, F2, 9) (dual of [1044, 1001, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(243, 1045, F2, 9) (dual of [1045, 1002, 10]-code), using
- construction XX applied to C1 = C([1021,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([1021,6]) [i] based on
- linear OA(231, 1023, F2, 7) (dual of [1023, 992, 8]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(231, 1023, F2, 7) (dual of [1023, 992, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(241, 1023, F2, 9) (dual of [1023, 982, 10]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(221, 1023, F2, 5) (dual of [1023, 1002, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code) (see above)
- construction XX applied to C1 = C([1021,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([1021,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(243, 1045, F2, 9) (dual of [1045, 1002, 10]-code), using
- OOA 3-folding [i] based on linear OA(243, 1044, F2, 9) (dual of [1044, 1001, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(243, 348, F2, 3, 9) (dual of [(348, 3), 1001, 10]-NRT-code), using
- linear OOA(2208, 1677720, F2, 5, 19) (dual of [(1677720, 5), 8388392, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 5-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
Mode: 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(2251, 1678068, F2, 6, 19) (dual of [(1678068, 6), 10068157, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2251, 1678068, F2, 7, 19) (dual of [(1678068, 7), 11746225, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(2251, 1678068, F2, 8, 19) (dual of [(1678068, 8), 13424293, 20]-NRT-code) | [i] | ||
| 4 | Digital (232, 251, 1678068)-net over F2 | [i] | ||