Information on Result #700505
Linear OA(261, 72, F2, 29) (dual of [72, 11, 30]-code), using construction XX applied to C([0,27]) ⊂ 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(257, 63, F2, 31) (dual of [63, 6, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 32 [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(21, 6, F2, 1) (dual of [6, 5, 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, 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 (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
None.