MinT - Information on Result #735204

Information on Result #735204

Linear OA(81⁷⁷, 6745, F₈₁, 28) (dual of [6745, 6668, 29]-code), using (u,Â u+v)-construction based on

linear OA(81²², 182, F₈₁, 14) (dual of [182, 160, 15]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(81⁷, 82, F₈₁, 7) (dual of [82, 75, 8]-code or 82-arc in PG(6,81)), using
    - extended Reedâ€“Solomon code RS_e(75,81) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 82Â | 81²âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
  2. linear OA(81¹⁵, 100, F₈₁, 14) (dual of [100, 85, 15]-code), using
    - extended algebraic-geometric code AG_e(F,85P) [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(81⁵⁵, 6563, F₈₁, 28) (dual of [6563, 6508, 29]-code), using
- constructionÂ X applied to C_e(27) âŠ‚ C_e(26) [i] based on
  1. linear OA(81⁵⁵, 6561, F₈₁, 28) (dual of [6561, 6506, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
  2. linear OA(81⁵³, 6561, F₈₁, 27) (dual of [6561, 6508, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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(81⁷⁷, 3372, F₈₁, 2, 28) (dual of [(3372, 2), 6667, 29]-NRT-code)	[i]		OOA Folding
2	Linear OOA(81⁷⁷, 2248, F₈₁, 3, 28) (dual of [(2248, 3), 6667, 29]-NRT-code)	[i]		OOA Folding