Information on Result #702237

Linear OA(293, 531, F2, 21) (dual of [531, 438, 22]-code), using construction XX applied to C1 = C([509,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([509,18]) based on
  1. linear OA(282, 511, F2, 19) (dual of [511, 429, 20]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
  2. linear OA(282, 511, F2, 19) (dual of [511, 429, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
  3. linear OA(291, 511, F2, 21) (dual of [511, 420, 22]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
  4. linear OA(273, 511, F2, 17) (dual of [511, 438, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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(292, 530, F2, 20) (dual of [530, 438, 21]-code) [i]Truncation
2Linear OOA(293, 265, F2, 2, 21) (dual of [(265, 2), 437, 22]-NRT-code) [i]OOA Folding
3Linear OOA(293, 177, F2, 3, 21) (dual of [(177, 3), 438, 22]-NRT-code) [i]
4Linear OOA(293, 132, F2, 4, 21) (dual of [(132, 4), 435, 22]-NRT-code) [i]
5Linear OOA(293, 106, F2, 5, 21) (dual of [(106, 5), 437, 22]-NRT-code) [i]
6Linear OOA(293, 88, F2, 6, 21) (dual of [(88, 6), 435, 22]-NRT-code) [i]
7Linear OOA(293, 75, F2, 7, 21) (dual of [(75, 7), 432, 22]-NRT-code) [i]