Information on Result #700511
Linear OA(275, 86, F2, 35) (dual of [86, 11, 36]-code), using construction XX applied to C({0,1,3,5,7,11,13,15,21,23,27,31}) ⊂ C({0,1,3,5,7,11,13,15,21,23,27}) ⊂ C({0,1,3,5,7,11,13,15,23,27}) based on
- linear OA(260, 63, F2, 35) (dual of [63, 3, 36]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,3,5,7,11,13,15,21,23,27,31}, and minimum distance d ≥ |{−26,−25,…,8}|+1 = 36 (BCH-bound) [i]
- linear OA(254, 63, F2, 27) (dual of [63, 9, 28]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,3,5,7,11,13,15,21,23,27}, and minimum distance d ≥ |{10,21,32,…,−19}|+1 = 28 (BCH-bound) [i]
- linear OA(252, 63, F2, 25) (dual of [63, 11, 26]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,3,5,7,11,13,15,23,27}, and minimum distance d ≥ |{−31,−20,−9,…,−19}|+1 = 26 (BCH-bound) [i]
- linear OA(212, 20, F2, 7) (dual of [20, 8, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 24, F2, 7) (dual of [24, 12, 8]-code), using
- extended Golay code Ge(2) [i]
- discarding factors / shortening the dual code based on linear OA(212, 24, F2, 7) (dual of [24, 12, 8]-code), using
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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
None.