Information on Result #733288

Linear OA(2770, 840, F27, 25) (dual of [840, 770, 26]-code), using (u, u+v)-construction based on
  1. linear OA(2721, 108, F27, 12) (dual of [108, 87, 13]-code), using
    • construction XX applied to C1 = C([103,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([103,10]) [i] based on
      1. linear OA(2719, 104, F27, 11) (dual of [104, 85, 12]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
      2. linear OA(2719, 104, F27, 11) (dual of [104, 85, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
      3. linear OA(2721, 104, F27, 12) (dual of [104, 83, 13]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
      4. linear OA(2717, 104, F27, 10) (dual of [104, 87, 11]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
      5. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
  2. linear OA(2749, 732, F27, 25) (dual of [732, 683, 26]-code), using
    • construction XX applied to C1 = C([727,22]), C2 = C([0,23]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([727,23]) [i] based on
      1. linear OA(2747, 728, F27, 24) (dual of [728, 681, 25]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,22}, and designed minimum distance d ≥ |I|+1 = 25 [i]
      2. linear OA(2747, 728, F27, 24) (dual of [728, 681, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [i]
      3. linear OA(2749, 728, F27, 25) (dual of [728, 679, 26]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,23}, and designed minimum distance d ≥ |I|+1 = 26 [i]
      4. linear OA(2745, 728, F27, 23) (dual of [728, 683, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
      5. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
      6. linear OA(270, 2, F27, 0) (dual of [2, 2, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(2770, 420, F27, 2, 25) (dual of [(420, 2), 770, 26]-NRT-code) [i]OOA Folding