Information on Result #672471
Linear OA(253, 131091, F2, 7) (dual of [131091, 131038, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(4) based on
- linear OA(252, 131072, F2, 7) (dual of [131072, 131020, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(235, 131072, F2, 5) (dual of [131072, 131037, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(218, 19, F2, 17) (dual of [19, 1, 18]-code), using
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- dual of repetition code with length 19 [i]
- strength reduction [i] based on linear OA(218, 19, F2, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
- linear OA(21, 19, F2, 1) (dual of [19, 18, 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(253, 131091, F2, 6) (dual of [131091, 131038, 7]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(254, 131092, F2, 7) (dual of [131092, 131038, 8]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(252, 131090, F2, 6) (dual of [131090, 131038, 7]-code) | [i] | Truncation | |