Information on Result #737131

Linear OA(3107, 276, F3, 31) (dual of [276, 169, 32]-code), using construction XX applied to Ce(30) ⊂ Ce(22) ⊂ Ce(21) based on
  1. linear OA(391, 243, F3, 31) (dual of [243, 152, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(376, 243, F3, 23) (dual of [243, 167, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  3. linear OA(371, 243, F3, 22) (dual of [243, 172, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
  4. linear OA(314, 31, F3, 7) (dual of [31, 17, 8]-code), using
    • construction X applied to Ce(6) ⊂ Ce(4) [i] based on
      1. linear OA(313, 27, F3, 7) (dual of [27, 14, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(310, 27, F3, 5) (dual of [27, 17, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
      3. linear OA(31, 4, F3, 1) (dual of [4, 3, 2]-code), using
  5. linear OA(30, 2, F3, 0) (dual of [2, 2, 1]-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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(3107, 138, F3, 2, 31) (dual of [(138, 2), 169, 32]-NRT-code) [i]OOA Folding