MinT - Information on Result #1302155

Information on Result #1302155

Linear OA(7⁷⁰, 81, F₇, 48) (dual of [81, 11, 49]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁶⁹, 79, F₇, 48) (dual of [79, 10, 49]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(7⁶³, 71, F₇, 48) (dual of [71, 8, 49]-code), using
    - 1 times truncation [i] based on linear OA(7⁶⁴, 72, F₇, 49) (dual of [72, 8, 50]-code), using
      - a quasi-cyclic or quasi-twisted code by Daskalov and Gulliver [i]
  2. linear OA(7⁶³, 73, F₇, 43) (dual of [73, 10, 44]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁶³Â > V_b^sâˆ’1(kâˆ’1)Â = 101686 390413 253398 637221 906493 467062 667469 681329 171649 [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(7⁶⁹, 80, F₇, 47) (dual of [80, 11, 48]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁶⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 15016 729271 727850 174403 639668 412093 539251 354842 834335 563319 [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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