MinT - Information on Result #1302170

Information on Result #1302170

Linear OA(7⁷⁴, 85, F₇, 51) (dual of [85, 11, 52]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁷³, 83, F₇, 51) (dual of [83, 10, 52]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(7⁶⁸, 76, F₇, 51) (dual of [76, 8, 52]-code), using
    - 4 times truncation [i] based on linear OA(7⁷², 80, F₇, 55) (dual of [80, 8, 56]-code), using
      - a quasi-cyclic or quasi-twisted code by Daskalov and Gulliver [i]
  2. linear OA(7⁶⁸, 78, F₇, 47) (dual of [78, 10, 48]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁶⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 2619 030375 884646 516970 607290 004551 829187 323214 220132 119271 [i]
  3. linear OA(7³, 5, F₇, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,7) or 5-cap in PG(2,7)), using
    - discarding factors / shortening the dual code based on linear OA(7³, 7, F₇, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
      - Reedâ€“Solomon code RS(4,7) [i]
linear OA(7⁷³, 84, F₇, 50) (dual of [84, 11, 51]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁷³Â > V_b^sâˆ’1(kâˆ’1)Â = 38 443376 224971 414135 388794 084919 272537 715136 001226 757714 035159 [i]
linear OA(7⁰, 1, F₇, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]

Mode: Linear.

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