Information on Result #672710
Linear OA(2224, 16439, F2, 31) (dual of [16439, 16215, 32]-code), using construction X applied to Ce(30) ⊂ Ce(24) based on
- linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2169, 16384, F2, 25) (dual of [16384, 16215, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(213, 55, F2, 5) (dual of [55, 42, 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 OA(2224, 16439, F2, 30) (dual of [16439, 16215, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2225, 16440, F2, 31) (dual of [16440, 16215, 32]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2223, 16438, F2, 30) (dual of [16438, 16215, 31]-code) | [i] | Truncation | |
| 4 | Linear OOA(2224, 8219, F2, 2, 31) (dual of [(8219, 2), 16214, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2224, 5479, F2, 3, 31) (dual of [(5479, 3), 16213, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2224, 4109, F2, 4, 31) (dual of [(4109, 4), 16212, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(2224, 3287, F2, 5, 31) (dual of [(3287, 5), 16211, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(2224, 2739, F2, 6, 31) (dual of [(2739, 6), 16210, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(2224, 2348, F2, 7, 31) (dual of [(2348, 7), 16212, 32]-NRT-code) | [i] | ||