MinT - Information on Result #735425

Information on Result #735425

Linear OA(81⁵⁴, 531626, F₈₁, 15) (dual of [531626, 531572, 16]-code), using (u,Â u+v)-construction based on

linear OA(81¹¹, 182, F₈₁, 7) (dual of [182, 171, 8]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(81³, 82, F₈₁, 3) (dual of [82, 79, 4]-code or 82-arc in PG(2,81) or 82-cap in PG(2,81)), using
    - extended Reedâ€“Solomon code RS_e(79,81) [i]
    - oval in PG(2,Â 81) [i]
  2. linear OA(81⁸, 100, F₈₁, 7) (dual of [100, 92, 8]-code), using
    - extended algebraic-geometric code AG_e(F,92P) [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(81⁴³, 531444, F₈₁, 15) (dual of [531444, 531401, 16]-code), using
- constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
  1. linear OA(81⁴³, 531441, F₈₁, 15) (dual of [531441, 531398, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
  2. linear OA(81⁴⁰, 531441, F₈₁, 14) (dual of [531441, 531401, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
  3. linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 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(81⁵⁴, 265813, F₈₁, 2, 15) (dual of [(265813, 2), 531572, 16]-NRT-code)	[i]		OOA Folding