Information on Result #661427

Linear OA(2204, 216, F2, 97) (dual of [216, 12, 98]-code), using concatenation of two codes based on
  1. linear OA(466, 72, F4, 48) (dual of [72, 6, 49]-code), using
    • discarding factors / shortening the dual code based on linear OA(466, 73, F4, 48) (dual of [73, 7, 49]-code), using
      • 2 times truncation [i] based on linear OA(468, 75, F4, 50) (dual of [75, 7, 51]-code), using
        • construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,47}), C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43}), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43,47}) [i] based on
          1. linear OA(459, 63, F4, 46) (dual of [63, 4, 47]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,47}, and minimum distance d ≥ |{−4,−3,…,41}|+1 = 47 (BCH-bound) [i]
          2. linear OA(459, 63, F4, 46) (dual of [63, 4, 47]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43}, and minimum distance d ≥ |{1,6,11,…,−26}|+1 = 47 (BCH-bound) [i]
          3. linear OA(462, 63, F4, 62) (dual of [63, 1, 63]-code or 63-arc in PG(61,4)), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,23,26,27,30,31,43,47}, and minimum distance d ≥ |{1,23,45,…,20}|+1 = 63 (BCH-bound) [i]
          4. linear OA(456, 63, F4, 42) (dual of [63, 7, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 43 [i]
          5. linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
          6. linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)) (see above)
  2. linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), 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 OOA(2204, 108, F2, 2, 97) (dual of [(108, 2), 12, 98]-NRT-code) [i]OOA Folding
2Linear OOA(2204, 72, F2, 3, 97) (dual of [(72, 3), 12, 98]-NRT-code) [i]