Information on Result #673840
Linear OA(2140, 272, F2, 39) (dual of [272, 132, 40]-code), using construction XX applied to Ce(38) ⊂ Ce(36) ⊂ Ce(30) based on
- linear OA(2133, 256, F2, 39) (dual of [256, 123, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2125, 256, F2, 37) (dual of [256, 131, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2117, 256, F2, 31) (dual of [256, 139, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 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
- linear OA(25, 6, F2, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,2)), using
- dual of repetition code with length 6 [i]
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(2140, 272, F2, 38) (dual of [272, 132, 39]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2141, 273, F2, 39) (dual of [273, 132, 40]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2139, 271, F2, 38) (dual of [271, 132, 39]-code) | [i] | Truncation | |
| 4 | Linear OOA(2140, 136, F2, 2, 39) (dual of [(136, 2), 132, 40]-NRT-code) | [i] | OOA Folding | |