Information on Result #1012158

Linear OOA(4246, 2796545, F4, 3, 23) (dual of [(2796545, 3), 8389389, 24]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(441, 344, F4, 3, 11) (dual of [(344, 3), 991, 12]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(441, 1032, F4, 11) (dual of [1032, 991, 12]-code), using
      • discarding factors / shortening the dual code based on linear OA(441, 1033, F4, 11) (dual of [1033, 992, 12]-code), using
        • construction XX applied to C1 = C([1022,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([1022,9]) [i] based on
          1. linear OA(436, 1023, F4, 10) (dual of [1023, 987, 11]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
          2. linear OA(436, 1023, F4, 10) (dual of [1023, 987, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
          3. linear OA(441, 1023, F4, 11) (dual of [1023, 982, 12]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
          4. linear OA(431, 1023, F4, 9) (dual of [1023, 992, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
          5. linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
          6. linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code) (see above)
  2. linear OOA(4205, 2796201, F4, 3, 23) (dual of [(2796201, 3), 8388398, 24]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(4205, large, F4, 23) (dual of [large, large−205, 24]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.