MinT - Information on Result #1082804

Information on Result #1082804

Linear OOA(81⁷², 1840, F₈₁, 4, 26) (dual of [(1840, 4), 7288, 27]-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(81⁵¹, 1640, F₈₁, 4, 26) (dual of [(1640, 4), 6509, 27]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81⁵¹, 6560, F₈₁, 26) (dual of [6560, 6509, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁵¹, 6561, F₈₁, 26) (dual of [6561, 6510, 27]-code), using
    - an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

Mode: Constructive and linear.

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