MinT - Information on Result #663388

Information on Result #663388

Linear OA(7⁵⁵, 823554, F₇, 9) (dual of [823554, 823499, 10]-code), using (u,Â u+v)-construction based on

linear OA(7⁵, 11, F₇, 4) (dual of [11, 6, 5]-code), using
- constructionÂ X applied to AG(F, Q+0P) âŠ‚ AG(F, Q+1P) [i] based on
  1. linear OA(7⁴, 8, F₇, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8, using the rational function field F₇(x) [i]
  2. linear OA(7², 8, F₇, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using algebraic-geometric code AG(F, Q+1P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8 (see above)
  3. linear OA(7¹, 3, F₇, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(7¹, s, F₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(7⁵⁰, 823543, F₇, 9) (dual of [823543, 823493, 10]-code), using
- an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

None.

None.