Information on Result #700589
Linear OA(262, 147, F2, 17) (dual of [147, 85, 18]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,63}), C2 = C([1,13]), C3 = C1 + C2 = C([1,11]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,63}) based on
- linear OA(250, 127, F2, 15) (dual of [127, 77, 16]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,63}, and minimum distance d ≥ |{−2,−1,…,12}|+1 = 16 (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(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(242, 127, F2, 12) (dual of [127, 85, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(24, 12, F2, 2) (dual of [12, 8, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- Hamming code H(4,2) [i]
- discarding factors / shortening the dual code based on linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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.
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 OA(261, 146, F2, 16) (dual of [146, 85, 17]-code) | [i] | Truncation | |
| 2 | Linear OOA(262, 49, F2, 3, 17) (dual of [(49, 3), 85, 18]-NRT-code) | [i] | OOA Folding | |