Information on Result #702200

Linear OA(257, 531, F2, 13) (dual of [531, 474, 14]-code), using construction XX applied to C1 = C([509,8]), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([509,10]) based on
  1. linear OA(246, 511, F2, 11) (dual of [511, 465, 12]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
  2. linear OA(246, 511, F2, 11) (dual of [511, 465, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(255, 511, F2, 13) (dual of [511, 456, 14]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
  4. linear OA(237, 511, F2, 9) (dual of [511, 474, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
  5. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
  6. linear OA(21, 10, F2, 1) (dual of [10, 9, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(256, 530, F2, 12) (dual of [530, 474, 13]-code) [i]Truncation
2Linear OOA(257, 265, F2, 2, 13) (dual of [(265, 2), 473, 14]-NRT-code) [i]OOA Folding
3Linear OOA(257, 177, F2, 3, 13) (dual of [(177, 3), 474, 14]-NRT-code) [i]
4Linear OOA(257, 132, F2, 4, 13) (dual of [(132, 4), 471, 14]-NRT-code) [i]
5Linear OOA(257, 106, F2, 5, 13) (dual of [(106, 5), 473, 14]-NRT-code) [i]
6Linear OOA(257, 88, F2, 6, 13) (dual of [(88, 6), 471, 14]-NRT-code) [i]