Information on Result #1584302
Linear OOA(243, 2097174, F2, 4, 4) (dual of [(2097174, 4), 8388653, 5]-NRT-code), using appending kth column based on linear OOA(243, 2097174, F2, 3, 4) (dual of [(2097174, 3), 6291479, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(243, 2097174, F2, 4) (dual of [2097174, 2097131, 5]-code), using
- 1 times truncation [i] based on linear OA(244, 2097175, F2, 5) (dual of [2097175, 2097131, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(243, 2097152, F2, 5) (dual of [2097152, 2097109, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(222, 2097152, F2, 3) (dual of [2097152, 2097130, 4]-code or 2097152-cap in PG(21,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(222, 23, F2, 21) (dual of [23, 1, 22]-code), using
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- dual of repetition code with length 23 [i]
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- linear OA(21, 23, F2, 1) (dual of [23, 22, 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
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- 1 times truncation [i] based on linear OA(244, 2097175, F2, 5) (dual of [2097175, 2097131, 6]-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(243, 2097174, F2, 5, 4) (dual of [(2097174, 5), 10485827, 5]-NRT-code) | [i] | Appending Arbitrary Columns | |
| 2 | Linear OOA(243, 2097174, F2, 6, 4) (dual of [(2097174, 6), 12583001, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(243, 2097174, F2, 7, 4) (dual of [(2097174, 7), 14680175, 5]-NRT-code) | [i] | ||
| 4 | Linear OOA(243, 2097174, F2, 8, 4) (dual of [(2097174, 8), 16777349, 5]-NRT-code) | [i] | ||
| 5 | Digital (39, 43, 2097174)-net over F2 | [i] | Net Defined by OOA | |