MinT - Information on Result #735337

Information on Result #735337

Linear OA(81⁷⁴, 531626, F₈₁, 20) (dual of [531626, 531552, 21]-code), using (u,Â u+v)-construction based on

linear OA(81¹⁶, 182, F₈₁, 10) (dual of [182, 166, 11]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(81⁵, 82, F₈₁, 5) (dual of [82, 77, 6]-code or 82-arc in PG(4,81)), using
    - extended Reedâ€“Solomon code RS_e(77,81) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 82Â | 81²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
  2. linear OA(81¹¹, 100, F₈₁, 10) (dual of [100, 89, 11]-code), using
    - extended algebraic-geometric code AG_e(F,89P) [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(81⁵⁸, 531444, F₈₁, 20) (dual of [531444, 531386, 21]-code), using
- constructionÂ X applied to C_e(19) âŠ‚ C_e(18) [i] based on
  1. linear OA(81⁵⁸, 531441, F₈₁, 20) (dual of [531441, 531383, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
  2. linear OA(81⁵⁵, 531441, F₈₁, 19) (dual of [531441, 531386, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(81⁷⁴, 265813, F₈₁, 2, 20) (dual of [(265813, 2), 531552, 21]-NRT-code)	[i]		OOA Folding
2	Linear OOA(81⁷⁴, 177208, F₈₁, 3, 20) (dual of [(177208, 3), 531550, 21]-NRT-code)	[i]		OOA Folding