MinT - Information on Result #904573

Information on Result #904573

Linear OOA(81⁴⁹, 3399, F₈₁, 2, 19) (dual of [(3399, 2), 6749, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹¹, 116, F₈₁, 2, 9) (dual of [(116, 2), 221, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,222P) [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(81³⁸, 3283, F₈₁, 2, 19) (dual of [(3283, 2), 6528, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81³⁸, 6566, F₈₁, 19) (dual of [6566, 6528, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(81³⁸, 6567, F₈₁, 19) (dual of [6567, 6529, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,8]) [i] based on
      1. linear OA(81³⁷, 6562, F₈₁, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      2. 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]
      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(81⁴⁹, 1699, F₈₁, 4, 19) (dual of [(1699, 4), 6747, 20]-NRT-code)	[i]		OOA Folding