Information on Result #672550
Linear OA(2152, 65575, F2, 19) (dual of [65575, 65423, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
- linear OA(2145, 65536, F2, 19) (dual of [65536, 65391, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2113, 65536, F2, 15) (dual of [65536, 65423, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-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(2152, 65575, F2, 18) (dual of [65575, 65423, 19]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2153, 65576, F2, 19) (dual of [65576, 65423, 20]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2151, 65574, F2, 18) (dual of [65574, 65423, 19]-code) | [i] | Truncation | |
| 4 | Linear OOA(2152, 32787, F2, 2, 19) (dual of [(32787, 2), 65422, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2152, 21858, F2, 3, 19) (dual of [(21858, 3), 65422, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(2152, 16393, F2, 4, 19) (dual of [(16393, 4), 65420, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(2152, 13115, F2, 5, 19) (dual of [(13115, 5), 65423, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(2152, 10929, F2, 6, 19) (dual of [(10929, 6), 65422, 20]-NRT-code) | [i] | ||
| 9 | Linear OOA(2152, 9367, F2, 7, 19) (dual of [(9367, 7), 65417, 20]-NRT-code) | [i] | ||
| 10 | Linear OOA(2152, 7286, F2, 19, 19) (dual of [(7286, 19), 138282, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |