MinT - Information on Result #1082633

Information on Result #1082633

Linear OOA(81⁴⁷, 1840, F₈₁, 4, 17) (dual of [(1840, 4), 7313, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁴, 200, F₈₁, 4, 8) (dual of [(200, 4), 786, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OOA(81⁹, 100, F₈₁, 4, 8) (dual of [(100, 4), 391, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,391P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100 (see above)
linear OOA(81³³, 1640, F₈₁, 4, 17) (dual of [(1640, 4), 6527, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81³³, 6560, F₈₁, 17) (dual of [6560, 6527, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(81³³, 6561, F₈₁, 17) (dual of [6561, 6528, 18]-code), using
    - an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

None.

None.