Information on Result #707054

Linear OA(4139, 259, F4, 52) (dual of [259, 120, 53]-code), using construction XX applied to C1 = C([52,102]), C2 = C([51,101]), C3 = C1 + C2 = C([52,101]), and C∩ = C1 ∩ C2 = C([51,102]) based on
  1. linear OA(4137, 255, F4, 51) (dual of [255, 118, 52]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {52,53,…,102}, and designed minimum distance d ≥ |I|+1 = 52 [i]
  2. linear OA(4137, 255, F4, 51) (dual of [255, 118, 52]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {51,52,…,101}, and designed minimum distance d ≥ |I|+1 = 52 [i]
  3. linear OA(4139, 255, F4, 52) (dual of [255, 116, 53]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {51,52,…,102}, and designed minimum distance d ≥ |I|+1 = 53 [i]
  4. linear OA(4135, 255, F4, 50) (dual of [255, 120, 51]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {52,53,…,101}, and designed minimum distance d ≥ |I|+1 = 51 [i]
  5. linear OA(40, 2, F4, 0) (dual of [2, 2, 1]-code), using
  6. linear OA(40, 2, F4, 0) (dual of [2, 2, 1]-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(4139, 259, F4, 51) (dual of [259, 120, 52]-code) [i]Strength Reduction
2Linear OA(4141, 261, F4, 52) (dual of [261, 120, 53]-code) [i]Code Embedding in Larger Space
3Linear OA(4142, 262, F4, 52) (dual of [262, 120, 53]-code) [i]
4Linear OA(4138, 258, F4, 51) (dual of [258, 120, 52]-code) [i]Truncation
5Linear OA(4136, 256, F4, 49) (dual of [256, 120, 50]-code) [i]
6Linear OOA(4139, 129, F4, 2, 52) (dual of [(129, 2), 119, 53]-NRT-code) [i]OOA Folding
7Linear OOA(4139, 86, F4, 3, 52) (dual of [(86, 3), 119, 53]-NRT-code) [i]