Information on Result #709038

Linear OA(4213, 1084, F4, 52) (dual of [1084, 871, 53]-code), using construction XX applied to C1 = C([1017,40]), C2 = C([0,45]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([1017,45]) based on
  1. linear OA(4176, 1023, F4, 47) (dual of [1023, 847, 48]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−6,−5,…,40}, and designed minimum distance d ≥ |I|+1 = 48 [i]
  2. linear OA(4171, 1023, F4, 46) (dual of [1023, 852, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [i]
  3. linear OA(4196, 1023, F4, 52) (dual of [1023, 827, 53]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−6,−5,…,45}, and designed minimum distance d ≥ |I|+1 = 53 [i]
  4. linear OA(4151, 1023, F4, 41) (dual of [1023, 872, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
  5. linear OA(410, 34, F4, 5) (dual of [34, 24, 6]-code), using
  6. linear OA(47, 27, F4, 4) (dual of [27, 20, 5]-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(4214, 1085, F4, 52) (dual of [1085, 871, 53]-code) [i]Code Embedding in Larger Space
2Linear OA(4215, 1086, F4, 52) (dual of [1086, 871, 53]-code) [i]
3Linear OOA(4213, 542, F4, 2, 52) (dual of [(542, 2), 871, 53]-NRT-code) [i]OOA Folding