MinT - Information on Result #735368

Information on Result #735368

Linear OA(81⁴⁹, 6745, F₈₁, 18) (dual of [6745, 6696, 19]-code), using (u,Â u+v)-construction based on

linear OA(81¹⁴, 182, F₈₁, 9) (dual of [182, 168, 10]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(81⁴, 82, F₈₁, 4) (dual of [82, 78, 5]-code or 82-arc in PG(3,81)), using
    - extended Reedâ€“Solomon code RS_e(78,81) [i]
  2. linear OA(81¹⁰, 100, F₈₁, 9) (dual of [100, 90, 10]-code), using
    - extended algebraic-geometric code AG_e(F,90P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]
linear OA(81³⁵, 6563, F₈₁, 18) (dual of [6563, 6528, 19]-code), using
- constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
  1. linear OA(81³⁵, 6561, F₈₁, 18) (dual of [6561, 6526, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
  2. linear OA(81³³, 6561, F₈₁, 17) (dual of [6561, 6528, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
  3. linear OA(81⁰, 2, F₈₁, 0) (dual of [2, 2, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]

Mode: Constructive and 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:

	Result		This result only	Method
1	Linear OOA(81⁴⁹, 3372, F₈₁, 2, 18) (dual of [(3372, 2), 6695, 19]-NRT-code)	[i]		OOA Folding
2	Linear OOA(81⁴⁹, 2248, F₈₁, 3, 18) (dual of [(2248, 3), 6695, 19]-NRT-code)	[i]		OOA Folding