Information on Result #701151

Linear OA(430, 93, F4, 11) (dual of [93, 63, 12]-code), using construction XX applied to C1 = C({2,5,6,14,17,21,57}), C2 = C({2,5,6,7,14,17,21}), C3 = C1 + C2 = C({2,5,6,14,17,21}), and C∩ = C1 ∩ C2 = C({2,5,6,7,14,17,21,57}) based on
  1. linear OA(426, 85, F4, 10) (dual of [85, 59, 11]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,14,17,21,57}, and minimum distance d ≥ |{−7,−4,−1,…,20}|+1 = 11 (BCH-bound) [i]
  2. linear OA(426, 85, F4, 10) (dual of [85, 59, 11]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,7,14,17,21}, and minimum distance d ≥ |{−4,−1,2,…,23}|+1 = 11 (BCH-bound) [i]
  3. linear OA(430, 85, F4, 11) (dual of [85, 55, 12]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,7,14,17,21,57}, and minimum distance d ≥ |{−7,−4,−1,…,23}|+1 = 12 (BCH-bound) [i]
  4. linear OA(422, 85, F4, 9) (dual of [85, 63, 10]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,14,17,21}, and minimum distance d ≥ |{−4,−1,2,…,20}|+1 = 10 (BCH-bound) [i]
  5. linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
  6. linear OA(40, 4, F4, 0) (dual of [4, 4, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(4255, 16477, F4, 43) (dual of [16477, 16222, 44]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
2Linear OA(4248, 16477, F4, 42) (dual of [16477, 16229, 43]-code) [i]
3Linear OOA(430, 46, F4, 2, 11) (dual of [(46, 2), 62, 12]-NRT-code) [i]OOA Folding