Information on Result #1299468

Linear OA(3236, 269, F3, 123) (dual of [269, 33, 124]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3218, 250, F3, 123) (dual of [250, 32, 124]-code), using
    • construction X applied to Ce(124) ⊂ 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(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]
      3. linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
  2. linear OA(3218, 251, F3, 105) (dual of [251, 33, 106]-code), using Gilbert–VarÅ¡amov bound and bm = 3218 > Vbs−1(k−1) = 83 448670 601097 143187 589501 654795 335952 875513 534060 079064 953677 245261 510264 841220 781861 875757 473396 060521 [i]
  3. linear OA(317, 18, F3, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,3)), 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(3236, 269, F3, 122) (dual of [269, 33, 123]-code) [i]Strength Reduction
2Linear OA(3236, 269, F3, 121) (dual of [269, 33, 122]-code) [i]
3Linear OA(3236, 269, F3, 120) (dual of [269, 33, 121]-code) [i]
4Linear OA(3235, 268, F3, 122) (dual of [268, 33, 123]-code) [i]Truncation
5Linear OA(3234, 267, F3, 121) (dual of [267, 33, 122]-code) [i]
6Linear OA(3232, 265, F3, 119) (dual of [265, 33, 120]-code) [i]
7Linear OA(3229, 262, F3, 116) (dual of [262, 33, 117]-code) [i]