MinT - Information on Result #1082815

Information on Result #1082815

Linear OOA(81⁷⁴, 1840, F₈₁, 4, 27) (dual of [(1840, 4), 7286, 28]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81²¹, 200, F₈₁, 4, 13) (dual of [(200, 4), 779, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁷, 100, F₈₁, 4, 6) (dual of [(100, 4), 393, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,393P) [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(81¹⁴, 100, F₈₁, 4, 13) (dual of [(100, 4), 386, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,386P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100 (see above)
linear OOA(81⁵³, 1640, F₈₁, 4, 27) (dual of [(1640, 4), 6507, 28]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81⁵³, 6560, F₈₁, 27) (dual of [6560, 6507, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁵³, 6561, F₈₁, 27) (dual of [6561, 6508, 28]-code), using
    - an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]

Mode: Constructive and linear.

None.

None.