Information on Result #701052

Linear OA(444, 69, F4, 24) (dual of [69, 25, 25]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,47}), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,47}) based on
  1. linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,47}, and minimum distance d ≥ |{−1,0,…,21}|+1 = 24 (BCH-bound) [i]
  2. linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
  3. linear OA(444, 63, F4, 24) (dual of [63, 19, 25]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,47}, and minimum distance d ≥ |{−1,0,…,22}|+1 = 25 (BCH-bound) [i]
  4. linear OA(438, 63, F4, 22) (dual of [63, 25, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
  5. linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
  6. linear OA(40, 3, F4, 0) (dual of [3, 3, 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(452, 85, F4, 24) (dual of [85, 33, 25]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(453, 89, F4, 24) (dual of [89, 36, 25]-code) [i]
3Linear OA(450, 78, F4, 24) (dual of [78, 28, 25]-code) [i]Construction X with VarÅ¡amov Bound
4Linear OOA(444, 34, F4, 2, 24) (dual of [(34, 2), 24, 25]-NRT-code) [i]OOA Folding
5Linear OOA(444, 23, F4, 3, 24) (dual of [(23, 3), 25, 25]-NRT-code) [i]