Information on Result #672243
Linear OA(265, 2097175, F2, 7) (dual of [2097175, 2097110, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(4) based on
- linear OA(264, 2097152, F2, 7) (dual of [2097152, 2097088, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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, 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
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(265, 2097175, F2, 6) (dual of [2097175, 2097110, 7]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(266, 2097176, F2, 7) (dual of [2097176, 2097110, 8]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(264, 2097174, F2, 6) (dual of [2097174, 2097110, 7]-code) | [i] | Truncation | |