Information on Result #1299484

Linear OA(3250, 286, F3, 124) (dual of [286, 36, 125]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3219, 251, F3, 124) (dual of [251, 32, 125]-code), using
    • construction XX applied to Ce(124) ⊂ Ce(121) ⊂ Ce(120) [i] based on
      1. linear OA(3217, 243, F3, 125) (dual of [243, 26, 126]-code), using an extension Ce(124) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,124], and designed minimum distance d ≥ |I|+1 = 125 [i]
      2. linear OA(3212, 243, F3, 122) (dual of [243, 31, 123]-code), using an extension Ce(121) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,121], and designed minimum distance d ≥ |I|+1 = 122 [i]
      3. linear OA(3211, 243, F3, 121) (dual of [243, 32, 122]-code), using an extension Ce(120) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,120], and designed minimum distance d ≥ |I|+1 = 121 [i]
      4. linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
      5. linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
  2. linear OA(3219, 255, F3, 104) (dual of [255, 36, 105]-code), using Gilbert–VarÅ¡amov bound and bm = 3219 > Vbs−1(k−1) = 234 943058 329380 408985 252835 089530 863934 011731 334128 818377 695152 333184 688124 728829 823222 054244 223016 886841 [i]
  3. linear OA(327, 31, F3, 19) (dual of [31, 4, 20]-code), using

Mode: 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 OA(3250, 286, F3, 123) (dual of [286, 36, 124]-code) [i]Strength Reduction