Information on Result #1299253

Linear OA(3205, 6607, F3, 36) (dual of [6607, 6402, 37]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3201, 6602, F3, 36) (dual of [6602, 6401, 37]-code), using
    • construction X applied to C([0,18]) ⊂ C([0,15]) [i] based on
      1. linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
      2. linear OA(3161, 6562, F3, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
      3. linear OA(38, 40, F3, 4) (dual of [40, 32, 5]-code), using
  2. linear OA(3201, 6603, F3, 32) (dual of [6603, 6402, 33]-code), using Gilbert–VarÅ¡amov bound and bm = 3201 > Vbs−1(k−1) = 6269 583089 689536 024577 235575 326308 815882 771476 427047 936316 309751 218552 181986 918411 346083 916201 [i]
  3. linear OA(33, 4, F3, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), 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(3206, 6608, F3, 36) (dual of [6608, 6402, 37]-code) [i]Code Embedding in Larger Space