Information on Result #673792
Linear OA(2174, 266, F2, 53) (dual of [266, 92, 54]-code), using construction XX applied to Ce(52) ⊂ Ce(50) ⊂ Ce(46) based on
- 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(2165, 256, F2, 51) (dual of [256, 91, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2157, 256, F2, 47) (dual of [256, 99, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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(23, 4, F2, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,2) or 4-cap in PG(2,2)), using
- dual of repetition code with length 4 [i]
- caps in base b = 2 [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(2174, 266, F2, 52) (dual of [266, 92, 53]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2175, 267, F2, 53) (dual of [267, 92, 54]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2173, 265, F2, 52) (dual of [265, 92, 53]-code) | [i] | Truncation | |
| 4 | Linear OOA(2174, 133, F2, 2, 53) (dual of [(133, 2), 92, 54]-NRT-code) | [i] | OOA Folding | |