MinT - Information on Result #904706

Information on Result #904706

Linear OOA(81⁶⁹, 3399, F₈₁, 2, 27) (dual of [(3399, 2), 6729, 28]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁵, 116, F₈₁, 2, 13) (dual of [(116, 2), 217, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,218P) [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(81⁵⁴, 3283, F₈₁, 2, 27) (dual of [(3283, 2), 6512, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81⁵⁴, 6566, F₈₁, 27) (dual of [6566, 6512, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁵⁴, 6567, F₈₁, 27) (dual of [6567, 6513, 28]-code), using
    - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(81⁵³, 6562, F₈₁, 27) (dual of [6562, 6509, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      2. linear OA(81⁴⁹, 6562, F₈₁, 25) (dual of [6562, 6513, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (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(81⁶⁹, 1699, F₈₁, 4, 27) (dual of [(1699, 4), 6727, 28]-NRT-code)	[i]		OOA Folding