Information on Result #737288

Linear OA(4255, 16477, F4, 43) (dual of [16477, 16222, 44]-code), using construction X applied to Ce(42) ⊂ Ce(30) based on
  1. linear OA(4225, 16384, F4, 43) (dual of [16384, 16159, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
  2. linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  3. 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}) [i] 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(4256, 16478, F4, 43) (dual of [16478, 16222, 44]-code) [i]Code Embedding in Larger Space
2Linear OOA(4255, 8238, F4, 2, 43) (dual of [(8238, 2), 16221, 44]-NRT-code) [i]OOA Folding
3Linear OOA(4255, 5492, F4, 3, 43) (dual of [(5492, 3), 16221, 44]-NRT-code) [i]