Information on Result #2224062
Linear OA(2115, 524308, F2, 12) (dual of [524308, 524193, 13]-code), using 1 times truncation based on linear OA(2116, 524309, F2, 13) (dual of [524309, 524193, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2115, 524288, F2, 13) (dual of [524288, 524173, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(296, 524288, F2, 11) (dual of [524288, 524192, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(220, 21, F2, 19) (dual of [21, 1, 20]-code), using
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- dual of repetition code with length 21 [i]
- strength reduction [i] based on linear OA(220, 21, F2, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
- linear OA(21, 21, F2, 1) (dual of [21, 20, 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(2117, 524310, F2, 12) (dual of [524310, 524193, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2118, 524311, F2, 12) (dual of [524311, 524193, 13]-code) | [i] | ||
| 3 | Linear OA(2119, 524312, F2, 12) (dual of [524312, 524193, 13]-code) | [i] | ||
| 4 | Linear OOA(2115, 262154, F2, 2, 12) (dual of [(262154, 2), 524193, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2115, 174769, F2, 3, 12) (dual of [(174769, 3), 524192, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(2115, 131077, F2, 4, 12) (dual of [(131077, 4), 524193, 13]-NRT-code) | [i] | ||
| 7 | Linear OOA(2115, 104861, F2, 5, 12) (dual of [(104861, 5), 524190, 13]-NRT-code) | [i] | ||
| 8 | Linear OOA(2115, 87384, F2, 6, 12) (dual of [(87384, 6), 524189, 13]-NRT-code) | [i] | ||
| 9 | Linear OOA(2115, 87384, F2, 7, 12) (dual of [(87384, 7), 611573, 13]-NRT-code) | [i] | OA Folding and Stacking | |
| 10 | Linear OOA(2115, 87384, F2, 8, 12) (dual of [(87384, 8), 698957, 13]-NRT-code) | [i] | ||
| 11 | Linear OOA(2115, 87384, F2, 12, 12) (dual of [(87384, 12), 1048493, 13]-NRT-code) | [i] | ||