Information on Result #708150

Linear OA(4130, 1077, F4, 31) (dual of [1077, 947, 32]-code), using construction XX applied to C1 = C([1018,20]), C2 = C([0,25]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([1018,25]) based on
  1. linear OA(496, 1023, F4, 26) (dual of [1023, 927, 27]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,20}, and designed minimum distance d ≥ |I|+1 = 27 [i]
  2. linear OA(496, 1023, F4, 26) (dual of [1023, 927, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
  3. linear OA(4116, 1023, F4, 31) (dual of [1023, 907, 32]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,25}, and designed minimum distance d ≥ |I|+1 = 32 [i]
  4. linear OA(476, 1023, F4, 21) (dual of [1023, 947, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
  5. linear OA(47, 27, F4, 4) (dual of [27, 20, 5]-code), using
  6. linear OA(47, 27, F4, 4) (dual of [27, 20, 5]-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(4131, 1078, F4, 31) (dual of [1078, 947, 32]-code) [i]Code Embedding in Larger Space
2Linear OA(4132, 1079, F4, 31) (dual of [1079, 947, 32]-code) [i]
3Linear OOA(4130, 538, F4, 2, 31) (dual of [(538, 2), 946, 32]-NRT-code) [i]OOA Folding