Information on Result #700648

Linear OA(2122, 147, F2, 51) (dual of [147, 25, 52]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}), C2 = C([0,43]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}) based on
  1. linear OA(2106, 127, F2, 47) (dual of [127, 21, 48]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,63}, and minimum distance d ≥ |{−4,−3,…,42}|+1 = 48 (BCH-bound) [i]
  2. linear OA(2106, 127, F2, 47) (dual of [127, 21, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 48 [i]
  3. linear OA(2113, 127, F2, 51) (dual of [127, 14, 52]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}, and minimum distance d ≥ |{−4,−3,…,46}|+1 = 52 (BCH-bound) [i]
  4. linear OA(299, 127, F2, 43) (dual of [127, 28, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
  5. linear OA(24, 8, F2, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
  6. linear OA(25, 12, F2, 3) (dual of [12, 7, 4]-code or 12-cap in PG(4,2)), 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:

ResultThis
result
only		Method
1Linear OA(2121, 146, F2, 50) (dual of [146, 25, 51]-code) [i]Truncation
2Linear OOA(2122, 73, F2, 2, 51) (dual of [(73, 2), 24, 52]-NRT-code) [i]OOA Folding
3Linear OOA(2122, 49, F2, 3, 51) (dual of [(49, 3), 25, 52]-NRT-code) [i]