Information on Result #808126
Linear OOA(2179, 531, F2, 2, 35) (dual of [(531, 2), 883, 36]-NRT-code), using OOA 2-folding based on linear OA(2179, 1062, F2, 35) (dual of [1062, 883, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(2166, 1024, F2, 35) (dual of [1024, 858, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2141, 1024, F2, 29) (dual of [1024, 883, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(213, 38, F2, 5) (dual of [38, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-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(2179, 531, F2, 2, 34) (dual of [(531, 2), 883, 35]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2181, 532, F2, 2, 35) (dual of [(532, 2), 883, 36]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 3 | Linear OOA(2180, 531, F2, 2, 35) (dual of [(531, 2), 882, 36]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(2179, 531, F2, 3, 35) (dual of [(531, 3), 1414, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2179, 531, F2, 4, 35) (dual of [(531, 4), 1945, 36]-NRT-code) | [i] | ||
| 6 | Linear OOA(2179, 531, F2, 5, 35) (dual of [(531, 5), 2476, 36]-NRT-code) | [i] | ||
| 7 | Linear OOA(2179, 531, F2, 6, 35) (dual of [(531, 6), 3007, 36]-NRT-code) | [i] | ||
| 8 | Linear OOA(2179, 531, F2, 7, 35) (dual of [(531, 7), 3538, 36]-NRT-code) | [i] | ||
| 9 | Linear OOA(2179, 531, F2, 8, 35) (dual of [(531, 8), 4069, 36]-NRT-code) | [i] | ||
| 10 | Digital (144, 179, 531)-net over F2 | [i] | ||