Information on Result #1303751

Linear OA(16103, 131090, F16, 25) (dual of [131090, 130987, 26]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(16102, 131088, F16, 25) (dual of [131088, 130986, 26]-code), using
    • trace code [i] based on linear OA(25651, 65544, F256, 25) (dual of [65544, 65493, 26]-code), using
      • construction X applied to Ce(24) ⊂ Ce(21) [i] based on
        1. linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
        2. linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
        3. linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
  2. linear OA(16102, 131089, F16, 24) (dual of [131089, 130987, 25]-code), using Gilbert–VarÅ¡amov bound and bm = 16102 > Vbs−1(k−1) = 219 138627 191097 057956 555815 242398 947382 803458 196104 678552 366205 430529 459546 682521 258284 738191 702926 089881 315075 876094 058496 [i]
  3. linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-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 OOA(16103, 131090, F16, 2, 25) (dual of [(131090, 2), 262077, 26]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (78, 103, 131090)-net over F16 [i]
3Linear OOA(16103, 65545, F16, 2, 25) (dual of [(65545, 2), 130987, 26]-NRT-code) [i]OOA Folding