Information on Result #1299593

Linear OA(3249, 282, F3, 129) (dual of [282, 33, 130]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3233, 265, F3, 129) (dual of [265, 32, 130]-code), using
    • 2 times truncation [i] based on linear OA(3235, 267, F3, 131) (dual of [267, 32, 132]-code), using
      • construction XX applied to Ce(130) ⊂ Ce(121) ⊂ Ce(120) [i] based on
        1. linear OA(3222, 243, F3, 131) (dual of [243, 21, 132]-code), using an extension Ce(130) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,130], and designed minimum distance d ≥ |I|+1 = 131 [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(312, 23, F3, 8) (dual of [23, 11, 9]-code), using
        5. linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
  2. linear OA(3233, 266, F3, 113) (dual of [266, 33, 114]-code), using Gilbert–VarÅ¡amov bound and bm = 3233 > Vbs−1(k−1) = 987 782806 253861 446841 693749 508248 399458 558705 173196 755565 930422 022053 433330 794924 699844 505427 294610 267800 381667 [i]
  3. linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), 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(3249, 282, F3, 128) (dual of [282, 33, 129]-code) [i]Strength Reduction
2Linear OA(3249, 282, F3, 127) (dual of [282, 33, 128]-code) [i]
3Linear OA(3250, 283, F3, 129) (dual of [283, 33, 130]-code) [i]Code Embedding in Larger Space
4Linear OA(3248, 281, F3, 128) (dual of [281, 33, 129]-code) [i]Truncation
5Linear OA(3246, 279, F3, 126) (dual of [279, 33, 127]-code) [i]