Information on Result #2219740
Linear OA(250, 70, F2, 20) (dual of [70, 20, 21]-code), using 1 times truncation based on linear OA(251, 71, F2, 21) (dual of [71, 20, 22]-code), using
- construction XX applied to C1 = C({0,3,5,7,11,13,15,23,27}), C2 = C({0,3,5,7,9,11,13,15,23}), C3 = C1 + C2 = C({0,3,5,7,11,13,15,23}), and C∩ = C1 ∩ C2 = C({0,3,5,7,9,11,13,15,23,27}) [i] based on
- linear OA(246, 63, F2, 19) (dual of [63, 17, 20]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,3,5,7,11,13,15,23,27}, and minimum distance d ≥ |{23,28,33,…,−13}|+1 = 20 (BCH-bound) [i]
- linear OA(246, 63, F2, 19) (dual of [63, 17, 20]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,3,5,7,9,11,13,15,23}, and minimum distance d ≥ |{13,18,23,…,−23}|+1 = 20 (BCH-bound) [i]
- linear OA(249, 63, F2, 21) (dual of [63, 14, 22]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,3,5,7,9,11,13,15,23,27}, and minimum distance d ≥ |{13,18,23,…,−13}|+1 = 22 (BCH-bound) [i]
- linear OA(243, 63, F2, 17) (dual of [63, 20, 18]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,3,5,7,11,13,15,23}, and minimum distance d ≥ |{23,28,33,…,−23}|+1 = 18 (BCH-bound) [i]
- linear OA(21, 4, F2, 1) (dual of [4, 3, 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(21, 4, F2, 1) (dual of [4, 3, 2]-code) (see above)
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(250, 35, F2, 2, 20) (dual of [(35, 2), 20, 21]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(250, 23, F2, 3, 20) (dual of [(23, 3), 19, 21]-NRT-code) | [i] | ||