Information on Result #672757
Linear OA(2119, 8206, F2, 19) (dual of [8206, 8087, 20]-code), using construction X applied to Ce(18) ⊂ Ce(16) based on
- linear OA(2118, 8192, F2, 19) (dual of [8192, 8074, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2105, 8192, F2, 17) (dual of [8192, 8087, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(2119, 8206, F2, 18) (dual of [8206, 8087, 19]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2120, 8207, F2, 19) (dual of [8207, 8087, 20]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2121, 8208, F2, 19) (dual of [8208, 8087, 20]-code) | [i] | ||
| 4 | Linear OA(2122, 8209, F2, 19) (dual of [8209, 8087, 20]-code) | [i] | ||
| 5 | Linear OA(2123, 8210, F2, 19) (dual of [8210, 8087, 20]-code) | [i] | ||
| 6 | Linear OA(2118, 8205, F2, 18) (dual of [8205, 8087, 19]-code) | [i] | Truncation | |
| 7 | Linear OOA(2119, 4103, F2, 2, 19) (dual of [(4103, 2), 8087, 20]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2119, 2735, F2, 3, 19) (dual of [(2735, 3), 8086, 20]-NRT-code) | [i] | ||
| 9 | Linear OOA(2119, 2051, F2, 4, 19) (dual of [(2051, 4), 8085, 20]-NRT-code) | [i] | ||
| 10 | Linear OOA(2119, 1641, F2, 5, 19) (dual of [(1641, 5), 8086, 20]-NRT-code) | [i] | ||
| 11 | Linear OOA(2119, 1367, F2, 6, 19) (dual of [(1367, 6), 8083, 20]-NRT-code) | [i] | ||
| 12 | Linear OOA(2119, 1172, F2, 7, 19) (dual of [(1172, 7), 8085, 20]-NRT-code) | [i] | ||
| 13 | Linear OOA(2119, 1025, F2, 8, 19) (dual of [(1025, 8), 8081, 20]-NRT-code) | [i] | ||
| 14 | Linear OOA(2119, 911, F2, 19, 19) (dual of [(911, 19), 17190, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |