Information on Result #700512
Linear OA(221, 77, F2, 7) (dual of [77, 56, 8]-code), using construction XX applied to C1 = C({0,1,31}), C2 = C([0,3]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C({0,1,3,31}) based on
- linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,31}, and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(219, 63, F2, 7) (dual of [63, 44, 8]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,1,3,31}, and minimum distance d ≥ |{−2,−1,…,4}|+1 = 8 (BCH-bound) [i]
- linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(21, 7, F2, 1) (dual of [7, 6, 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, 7, F2, 1) (dual of [7, 6, 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
None.