Information on Result #2258172
Linear OA(2124, 32787, F2, 16) (dual of [32787, 32663, 17]-code), using 2 times code embedding in larger space based on linear OA(2122, 32785, F2, 16) (dual of [32785, 32663, 17]-code), using
- construction X4 applied to C([0,16]) ⊂ C([1,14]) [i] based on
- linear OA(2121, 32767, F2, 17) (dual of [32767, 32646, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2105, 32767, F2, 14) (dual of [32767, 32662, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
- dual of repetition code with length 18 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 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 OOA(2124, 10929, F2, 3, 16) (dual of [(10929, 3), 32663, 17]-NRT-code) | [i] | OOA Folding | |