Information on Result #672624
Linear OA(2239, 32826, F2, 31) (dual of [32826, 32587, 32]-code), using construction X applied to Ce(30) ⊂ Ce(24) based on
- linear OA(2226, 32768, F2, 31) (dual of [32768, 32542, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2181, 32768, F2, 25) (dual of [32768, 32587, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(213, 58, F2, 5) (dual of [58, 45, 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(2239, 32826, F2, 30) (dual of [32826, 32587, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2240, 32827, F2, 31) (dual of [32827, 32587, 32]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2238, 32825, F2, 30) (dual of [32825, 32587, 31]-code) | [i] | Truncation | |
| 4 | Linear OOA(2239, 16413, F2, 2, 31) (dual of [(16413, 2), 32587, 32]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2239, 10942, F2, 3, 31) (dual of [(10942, 3), 32587, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2239, 8206, F2, 4, 31) (dual of [(8206, 4), 32585, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(2239, 6565, F2, 5, 31) (dual of [(6565, 5), 32586, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(2239, 5471, F2, 6, 31) (dual of [(5471, 6), 32587, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(2239, 4689, F2, 7, 31) (dual of [(4689, 7), 32584, 32]-NRT-code) | [i] | ||
| 10 | Linear OOA(2239, 4103, F2, 8, 31) (dual of [(4103, 8), 32585, 32]-NRT-code) | [i] | ||
| 11 | Linear OOA(2239, 2188, F2, 31, 31) (dual of [(2188, 31), 67589, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |