Information on Result #701108

Linear OA(462, 78, F4, 34) (dual of [78, 16, 35]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,31,47}), C2 = C([0,27]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,31,47}) based on
  1. linear OA(453, 63, F4, 31) (dual of [63, 10, 32]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,31,47}, and minimum distance d ≥ |{−4,−3,…,26}|+1 = 32 (BCH-bound) [i]
  2. linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 31 [i]
  3. linear OA(456, 63, F4, 34) (dual of [63, 7, 35]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,31,47}, and minimum distance d ≥ |{−4,−3,…,29}|+1 = 35 (BCH-bound) [i]
  4. linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
  5. linear OA(44, 10, F4, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,4)), using
  6. linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), 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.

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Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(461, 77, F4, 33) (dual of [77, 16, 34]-code) [i]Truncation
2Linear OA(4138, 152, F4, 69) (dual of [152, 14, 70]-code) [i]Repeating Each Code Word
3Linear OA(4137, 150, F4, 69) (dual of [150, 13, 70]-code) [i]
4Linear OA(4136, 148, F4, 69) (dual of [148, 12, 70]-code) [i]
5Linear OA(4135, 146, F4, 69) (dual of [146, 11, 70]-code) [i]
6Linear OA(463, 80, F4, 34) (dual of [80, 17, 35]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OOA(462, 39, F4, 2, 34) (dual of [(39, 2), 16, 35]-NRT-code) [i]OOA Folding
8Linear OOA(462, 26, F4, 3, 34) (dual of [(26, 3), 16, 35]-NRT-code) [i]