Information on Result #709351

Linear OA(4228, 1070, F4, 58) (dual of [1070, 842, 59]-code), using construction XX applied to C1 = C([1018,48]), C2 = C([0,52]), C3 = C1 + C2 = C([0,48]), and C∩ = C1 ∩ C2 = C([1018,52]) based on
  1. linear OA(4201, 1023, F4, 54) (dual of [1023, 822, 55]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,48}, and designed minimum distance d ≥ |I|+1 = 55 [i]
  2. linear OA(4196, 1023, F4, 53) (dual of [1023, 827, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
  3. linear OA(4216, 1023, F4, 58) (dual of [1023, 807, 59]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,52}, and designed minimum distance d ≥ |I|+1 = 59 [i]
  4. linear OA(4181, 1023, F4, 49) (dual of [1023, 842, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [i]
  5. linear OA(47, 27, F4, 4) (dual of [27, 20, 5]-code), using
  6. linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), 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(4229, 1071, F4, 58) (dual of [1071, 842, 59]-code) [i]Code Embedding in Larger Space
2Linear OOA(4228, 535, F4, 2, 58) (dual of [(535, 2), 842, 59]-NRT-code) [i]OOA Folding
3Linear OOA(4228, 356, F4, 3, 58) (dual of [(356, 3), 840, 59]-NRT-code) [i]