Information on Result #700542

Linear OA(260, 77, F2, 27) (dual of [77, 17, 28]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,31}), C2 = C([0,21]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,21,31}) based on
  1. 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 = {0,1,3,5,7,9,11,13,15,31}, and minimum distance d ≥ |{−4,−3,…,20}|+1 = 26 (BCH-bound) [i]
  2. linear OA(248, 63, F2, 23) (dual of [63, 15, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 24 [i]
  3. 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 = {0,1,3,5,7,9,11,13,15,21,31}, and minimum distance d ≥ |{−4,−3,…,22}|+1 = 28 (BCH-bound) [i]
  4. linear OA(246, 63, F2, 21) (dual of [63, 17, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 22 [i]
  5. linear OA(25, 11, F2, 3) (dual of [11, 6, 4]-code or 11-cap in PG(4,2)), using
  6. linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), 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(259, 76, F2, 26) (dual of [76, 17, 27]-code) [i]Truncation
2Linear OOA(260, 38, F2, 2, 27) (dual of [(38, 2), 16, 28]-NRT-code) [i]OOA Folding