Information on Result #672852
Linear OA(274, 4110, F2, 13) (dual of [4110, 4036, 14]-code), using construction X4 applied to Ce(12) ⊂ Ce(10) based on
- linear OA(273, 4096, F2, 13) (dual of [4096, 4023, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(261, 4096, F2, 11) (dual of [4096, 4035, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(213, 14, F2, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), using
- dual of repetition code with length 14 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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(274, 4110, F2, 12) (dual of [4110, 4036, 13]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(275, 4111, F2, 13) (dual of [4111, 4036, 14]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(276, 4112, F2, 13) (dual of [4112, 4036, 14]-code) | [i] | ||
| 4 | Linear OA(277, 4113, F2, 13) (dual of [4113, 4036, 14]-code) | [i] | ||
| 5 | Linear OA(278, 4114, F2, 13) (dual of [4114, 4036, 14]-code) | [i] | ||
| 6 | Linear OA(273, 4109, F2, 12) (dual of [4109, 4036, 13]-code) | [i] | Truncation | |
| 7 | Linear OOA(274, 2055, F2, 2, 13) (dual of [(2055, 2), 4036, 14]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(274, 1370, F2, 3, 13) (dual of [(1370, 3), 4036, 14]-NRT-code) | [i] | ||
| 9 | Linear OOA(274, 822, F2, 5, 13) (dual of [(822, 5), 4036, 14]-NRT-code) | [i] | ||
| 10 | Linear OOA(274, 685, F2, 6, 13) (dual of [(685, 6), 4036, 14]-NRT-code) | [i] | ||