Information on Result #700564

Linear OA(231, 143, F2, 9) (dual of [143, 112, 10]-code), using construction XX applied to C1 = C({0,1,3,63}), C2 = C([0,5]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,3,5,63}) based on
  1. linear OA(222, 127, F2, 7) (dual of [127, 105, 8]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,63}, and minimum distance d ≥ |{−2,−1,…,4}|+1 = 8 (BCH-bound) [i]
  2. linear OA(222, 127, F2, 7) (dual of [127, 105, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]
  3. linear OA(229, 127, F2, 9) (dual of [127, 98, 10]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,63}, and minimum distance d ≥ |{−2,−1,…,6}|+1 = 10 (BCH-bound) [i]
  4. linear OA(215, 127, F2, 5) (dual of [127, 112, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
  5. linear OA(21, 8, F2, 1) (dual of [8, 7, 2]-code), using
  6. linear OA(21, 8, F2, 1) (dual of [8, 7, 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

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(230, 142, F2, 8) (dual of [142, 112, 9]-code) [i]Truncation
2Linear OOA(231, 71, F2, 2, 9) (dual of [(71, 2), 111, 10]-NRT-code) [i]OOA Folding
3Linear OOA(231, 47, F2, 3, 9) (dual of [(47, 3), 110, 10]-NRT-code) [i]
4Linear OOA(231, 35, F2, 4, 9) (dual of [(35, 4), 109, 10]-NRT-code) [i]