Information on Result #672250
Linear OA(2197, 2097201, F2, 19) (dual of [2097201, 2097004, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
- linear OA(2190, 2097152, F2, 19) (dual of [2097152, 2096962, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2148, 2097152, F2, 15) (dual of [2097152, 2097004, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), 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(2197, 2097201, F2, 18) (dual of [2097201, 2097004, 19]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2198, 2097202, F2, 19) (dual of [2097202, 2097004, 20]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2196, 2097200, F2, 18) (dual of [2097200, 2097004, 19]-code) | [i] | Truncation | |
| 4 | Linear OOA(2197, 1048600, F2, 2, 19) (dual of [(1048600, 2), 2097003, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2197, 699067, F2, 3, 19) (dual of [(699067, 3), 2097004, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(2197, 524300, F2, 4, 19) (dual of [(524300, 4), 2097003, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(2197, 419440, F2, 5, 19) (dual of [(419440, 5), 2097003, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(2197, 349533, F2, 6, 19) (dual of [(349533, 6), 2097001, 20]-NRT-code) | [i] | ||
| 9 | Linear OOA(2197, 299600, F2, 7, 19) (dual of [(299600, 7), 2097003, 20]-NRT-code) | [i] | ||
| 10 | Linear OOA(2197, 262150, F2, 8, 19) (dual of [(262150, 8), 2097003, 20]-NRT-code) | [i] | ||
| 11 | Linear OOA(2197, 233022, F2, 19, 19) (dual of [(233022, 19), 4427221, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |