MinT - Information on Result #1302219

Information on Result #1302219

Linear OA(7⁸², 93, F₇, 57) (dual of [93, 11, 58]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁸¹, 91, F₇, 57) (dual of [91, 10, 58]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(7⁷⁵, 83, F₇, 57) (dual of [83, 8, 58]-code), using
    - 5 times truncation [i] based on linear OA(7⁸⁰, 88, F₇, 62) (dual of [88, 8, 63]-code), using
      - a quasi-cyclic or quasi-twisted code by Daskalov and Gulliver [i]
  2. linear OA(7⁷⁵, 85, F₇, 52) (dual of [85, 10, 53]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁷⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 1583 206773 232801 420350 273521 618051 969940 155431 377400 226340 195553 [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(7⁸¹, 92, F₇, 56) (dual of [92, 11, 57]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁸¹Â > V_b^sâˆ’1(kâˆ’1)Â = 238 095211 512487 182012 064517 610897 014862 029320 569185 142077 879619 435799 [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.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(7⁸³, 95, F₇, 57) (dual of [95, 12, 58]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound