Information on Result #700601
Linear OA(269, 144, F2, 20) (dual of [144, 75, 21]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,63}), C2 = C([1,15]), C3 = C1 + C2 = C([1,13]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,63}) based on
- linear OA(257, 127, F2, 17) (dual of [127, 70, 18]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,63}, and minimum distance d ≥ |{−2,−1,…,14}|+1 = 18 (BCH-bound) [i]
- linear OA(256, 127, F2, 18) (dual of [127, 71, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(264, 127, F2, 21) (dual of [127, 63, 22]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,63}, and minimum distance d ≥ |{−2,−1,…,18}|+1 = 22 (BCH-bound) [i]
- linear OA(249, 127, F2, 14) (dual of [127, 78, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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(24, 8, F2, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(269, 48, F2, 3, 20) (dual of [(48, 3), 75, 21]-NRT-code) | [i] | OOA Folding | |