Information on Result #945929
Linear OOA(2173, 174769, F2, 3, 19) (dual of [(174769, 3), 524134, 20]-NRT-code), using OOA 3-folding based on linear OA(2173, 524307, F2, 19) (dual of [524307, 524134, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2173, 524308, F2, 19) (dual of [524308, 524135, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(2172, 524288, F2, 19) (dual of [524288, 524116, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2153, 524288, F2, 17) (dual of [524288, 524135, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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 X applied to Ce(18) ⊂ Ce(16) [i] based on
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 OOA(2173, 174769, F2, 3, 18) (dual of [(174769, 3), 524134, 19]-NRT-code) | [i] | Strength Reduction for OOAs | |