MinT - Information on Result #1082634

Information on Result #1082634

Linear OOA(81⁴⁴, 1757, F₈₁, 4, 17) (dual of [(1757, 4), 6984, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁰, 116, F₈₁, 4, 8) (dual of [(116, 4), 454, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,455P) [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
  - a function field by SÃ©mirat [i]
linear OOA(81³⁴, 1641, F₈₁, 4, 17) (dual of [(1641, 4), 6530, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81³⁴, 6564, F₈₁, 17) (dual of [6564, 6530, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(81³⁴, 6567, F₈₁, 17) (dual of [6567, 6533, 18]-code), using
    - constructionÂ X applied to C([0,8]) âŠ‚ C([0,7]) [i] based on
      1. linear OA(81³³, 6562, F₈₁, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      2. linear OA(81²⁹, 6562, F₈₁, 15) (dual of [6562, 6533, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      3. linear OA(81¹, 5, F₈₁, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(81⁴⁴, 878, F₈₁, 20, 17) (dual of [(878, 20), 17516, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row