Information on Result #702215

Linear OA(275, 532, F2, 16) (dual of [532, 457, 17]-code), using construction XX applied to C1 = C([509,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([509,14]) based on
  1. linear OA(264, 511, F2, 15) (dual of [511, 447, 16]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
  2. linear OA(263, 511, F2, 14) (dual of [511, 448, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  3. linear OA(273, 511, F2, 17) (dual of [511, 438, 18]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [i]
  4. linear OA(254, 511, F2, 12) (dual of [511, 457, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  5. linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
  6. linear OA(21, 10, F2, 1) (dual of [10, 9, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(276, 533, F2, 17) (dual of [533, 457, 18]-code) [i]Adding a Parity Check Bit
2Linear OOA(275, 266, F2, 2, 16) (dual of [(266, 2), 457, 17]-NRT-code) [i]OOA Folding
3Linear OOA(275, 177, F2, 3, 16) (dual of [(177, 3), 456, 17]-NRT-code) [i]
4Linear OOA(275, 133, F2, 4, 16) (dual of [(133, 4), 457, 17]-NRT-code) [i]
5Linear OOA(275, 76, F2, 7, 16) (dual of [(76, 7), 457, 17]-NRT-code) [i]