Information on Result #673783
Linear OA(2193, 274, F2, 59) (dual of [274, 81, 60]-code), using construction XX applied to Ce(58) ⊂ Ce(54) ⊂ Ce(52) based on
- linear OA(2185, 256, F2, 59) (dual of [256, 71, 60]-code), using an extension Ce(58) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,58], and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(2177, 256, F2, 55) (dual of [256, 79, 56]-code), using an extension Ce(54) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(2169, 256, F2, 53) (dual of [256, 87, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(25, 15, F2, 3) (dual of [15, 10, 4]-code or 15-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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(2192, 273, F2, 58) (dual of [273, 81, 59]-code) | [i] | Truncation | |
| 2 | Linear OOA(2193, 137, F2, 2, 59) (dual of [(137, 2), 81, 60]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2193, 91, F2, 3, 59) (dual of [(91, 3), 80, 60]-NRT-code) | [i] | ||