MinT - Information on Result #1302195

Information on Result #1302195

Linear OA(7⁷⁸, 89, F₇, 54) (dual of [89, 11, 55]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁷⁷, 87, F₇, 54) (dual of [87, 10, 55]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(7⁷¹, 79, F₇, 54) (dual of [79, 8, 55]-code), using
    - 1 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(7⁷¹, 81, F₇, 49) (dual of [81, 10, 50]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁷¹Â > V_b^sâˆ’1(kâˆ’1)Â = 646244 960790 229744 790668 788882 141632 929983 284748 803561 354113 [i]
  3. linear OA(7⁴, 6, F₇, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,7)), using
    - discarding factors / shortening the dual code based on linear OA(7⁴, 7, F₇, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,7)), using
      - Reedâ€“Solomon code RS(3,7) [i]
linear OA(7⁷⁷, 88, F₇, 53) (dual of [88, 11, 54]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁷⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 96498 387484 320104 916137 183381 283420 939124 998649 994557 300780 466551 [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.

None.

None.