Information on Result #678604

Linear OA(4122, 65563, F4, 19) (dual of [65563, 65441, 20]-code), using construction XX applied to C1 = C([0,8]), C2 = C([1,9]), C3 = C1 + C2 = C([1,8]), and C∩ = C1 ∩ C2 = C([0,9]) based on
  1. linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  2. linear OA(4112, 65537, F4, 10) (dual of [65537, 65425, 11]-code), using the narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [1,9], and minimum distance d ≥ |{−9,−7,−5,…,9}|+1 = 11 (BCH-bound) [i]
  3. linear OA(4113, 65537, F4, 19) (dual of [65537, 65424, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
  4. linear OA(496, 65537, F4, 8) (dual of [65537, 65441, 9]-code), using the narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  5. linear OA(48, 9, F4, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,4)), using
  6. linear OA(41, 17, F4, 1) (dual of [17, 16, 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 OOA(4122, 46127, F4, 2, 19) (dual of [(46127, 2), 92132, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4122, 46127, F4, 3, 19) (dual of [(46127, 3), 138259, 20]-NRT-code) [i]
3Digital (103, 122, 46127)-net over F4 [i]