Information on Result #1568416

Linear OOA(2243, 2796329, F2, 3, 19) (dual of [(2796329, 3), 8388744, 20]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(235, 128, F2, 3, 9) (dual of [(128, 3), 349, 10]-NRT-code), using
    • embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OOA(235, 128, F2, 2, 9) (dual of [(128, 2), 221, 10]-NRT-code), using
      • discarding factors / shortening the dual code based on linear OOA(235, 136, F2, 2, 9) (dual of [(136, 2), 237, 10]-NRT-code), using
        • OOA 2-folding [i] based on linear OA(235, 272, F2, 9) (dual of [272, 237, 10]-code), using
          • discarding factors / shortening the dual code based on linear OA(235, 273, F2, 9) (dual of [273, 238, 10]-code), using
            • construction XX applied to C1 = C([253,4]), C2 = C([0,6]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([253,6]) [i] based on
              1. linear OA(225, 255, F2, 7) (dual of [255, 230, 8]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
              2. linear OA(225, 255, F2, 7) (dual of [255, 230, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
              3. linear OA(233, 255, F2, 9) (dual of [255, 222, 10]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
              4. linear OA(217, 255, F2, 5) (dual of [255, 238, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
              5. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
              6. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code) (see above)
  2. linear OOA(2208, 2796201, F2, 3, 19) (dual of [(2796201, 3), 8388395, 20]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]

Mode: 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.