Information on Result #2666504
Linear OOA(275, 5467, F2, 3, 11) (dual of [(5467, 3), 16326, 12]-NRT-code), using 22 times duplication based on linear OOA(273, 5467, F2, 3, 11) (dual of [(5467, 3), 16328, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(273, 16401, F2, 11) (dual of [16401, 16328, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(272, 16400, F2, 11) (dual of [16400, 16328, 12]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(271, 16384, F2, 11) (dual of [16384, 16313, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(257, 16384, F2, 9) (dual of [16384, 16327, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(215, 16, F2, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
- dual of repetition code with length 16 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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 X4 applied to Ce(10) ⊂ Ce(8) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(272, 16400, F2, 11) (dual of [16400, 16328, 12]-code), 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 OOA(275, 4210, F2, 4, 11) (dual of [(4210, 4), 16765, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(275, 4210, F2, 5, 11) (dual of [(4210, 5), 20975, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(275, 4210, F2, 6, 11) (dual of [(4210, 6), 25185, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(275, 4210, F2, 7, 11) (dual of [(4210, 7), 29395, 12]-NRT-code) | [i] | ||
| 5 | Linear OOA(275, 4210, F2, 8, 11) (dual of [(4210, 8), 33605, 12]-NRT-code) | [i] | ||
| 6 | Digital (64, 75, 4210)-net over F2 | [i] | ||