MinT - Information on Result #1082315

Information on Result #1082315

Linear OOA(81²⁷, 132961, F₈₁, 4, 8) (dual of [(132961, 4), 531817, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81⁵, 100, F₈₁, 4, 4) (dual of [(100, 4), 395, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(81⁵, 100, F₈₁, 3, 4) (dual of [(100, 3), 295, 5]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,295P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]
linear OOA(81²², 132861, F₈₁, 4, 8) (dual of [(132861, 4), 531422, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81²², 531444, F₈₁, 8) (dual of [531444, 531422, 9]-code), using
  - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
    1. linear OA(81²², 531441, F₈₁, 8) (dual of [531441, 531419, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    2. linear OA(81¹⁹, 531441, F₈₁, 7) (dual of [531441, 531422, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(81²⁷, 132960, F₈₁, 12, 8) (dual of [(132960, 12), 1595493, 9]-NRT-code)	[i]		OOA Stacking with Additional Row