Information on Result #2175128
Linear OA(2193, 524310, F2, 21) (dual of [524310, 524117, 22]-code), using adding a parity check bit based on linear OA(2192, 524309, F2, 20) (dual of [524309, 524117, 21]-code), using
- construction X4 applied to C([0,20]) ⊂ C([1,18]) [i] based on
- linear OA(2191, 524287, F2, 21) (dual of [524287, 524096, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2171, 524287, F2, 18) (dual of [524287, 524116, 19]-code), using 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(221, 22, F2, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
- dual of repetition code with length 22 [i]
- linear OA(21, 22, F2, 1) (dual of [22, 21, 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(2193, 524310, F2, 20) (dual of [524310, 524117, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2194, 524311, F2, 21) (dual of [524311, 524117, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2195, 524312, F2, 21) (dual of [524312, 524117, 22]-code) | [i] | ||
| 4 | Linear OA(2196, 524313, F2, 21) (dual of [524313, 524117, 22]-code) | [i] | ||
| 5 | Linear OOA(2193, 262155, F2, 2, 21) (dual of [(262155, 2), 524117, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2193, 174770, F2, 3, 21) (dual of [(174770, 3), 524117, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(2193, 104862, F2, 5, 21) (dual of [(104862, 5), 524117, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(2193, 87385, F2, 6, 21) (dual of [(87385, 6), 524117, 22]-NRT-code) | [i] | ||