Information on Result #672747
Linear OA(2210, 8206, F2, 33) (dual of [8206, 7996, 34]-code), using construction X applied to Ce(32) ⊂ Ce(30) based on
- linear OA(2209, 8192, F2, 33) (dual of [8192, 7983, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(2210, 8206, F2, 32) (dual of [8206, 7996, 33]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2211, 8207, F2, 33) (dual of [8207, 7996, 34]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2212, 8208, F2, 33) (dual of [8208, 7996, 34]-code) | [i] | ||
| 4 | Linear OA(2213, 8209, F2, 33) (dual of [8209, 7996, 34]-code) | [i] | ||
| 5 | Linear OA(2214, 8210, F2, 33) (dual of [8210, 7996, 34]-code) | [i] | ||
| 6 | Linear OA(2209, 8205, F2, 32) (dual of [8205, 7996, 33]-code) | [i] | Truncation | |
| 7 | Linear OOA(2210, 4103, F2, 2, 33) (dual of [(4103, 2), 7996, 34]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2210, 2735, F2, 3, 33) (dual of [(2735, 3), 7995, 34]-NRT-code) | [i] | ||
| 9 | Linear OOA(2210, 2051, F2, 4, 33) (dual of [(2051, 4), 7994, 34]-NRT-code) | [i] | ||
| 10 | Linear OOA(2210, 1641, F2, 5, 33) (dual of [(1641, 5), 7995, 34]-NRT-code) | [i] | ||
| 11 | Linear OOA(2210, 1367, F2, 6, 33) (dual of [(1367, 6), 7992, 34]-NRT-code) | [i] | ||
| 12 | Linear OOA(2210, 1172, F2, 7, 33) (dual of [(1172, 7), 7994, 34]-NRT-code) | [i] | ||
| 13 | Linear OOA(2210, 1025, F2, 8, 33) (dual of [(1025, 8), 7990, 34]-NRT-code) | [i] | ||