Information on Result #672960
Linear OA(235, 2061, F2, 7) (dual of [2061, 2026, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(4) based on
- linear OA(234, 2048, F2, 7) (dual of [2048, 2014, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(223, 2048, F2, 5) (dual of [2048, 2025, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(212, 13, F2, 11) (dual of [13, 1, 12]-code), using
- strength reduction [i] based on linear OA(212, 13, F2, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
- dual of repetition code with length 13 [i]
- strength reduction [i] based on linear OA(212, 13, F2, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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(235, 2061, F2, 6) (dual of [2061, 2026, 7]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(236, 2062, F2, 7) (dual of [2062, 2026, 8]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(234, 2060, F2, 6) (dual of [2060, 2026, 7]-code) | [i] | Truncation | |