MinT - Information on Result #1302254

Information on Result #1302254

Linear OA(7⁹⁰, 101, F₇, 63) (dual of [101, 11, 64]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁸⁹, 99, F₇, 63) (dual of [99, 10, 64]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(7⁸³, 91, F₇, 63) (dual of [91, 8, 64]-code), using
    - 5 times truncation [i] based on linear OA(7⁸⁸, 96, F₇, 68) (dual of [96, 8, 69]-code), using
      - a quasi-cyclic or quasi-twisted code by Daskalov and Gulliver [i]
  2. linear OA(7⁸³, 93, F₇, 58) (dual of [93, 10, 59]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁸³Â > V_b^sâˆ’1(kâˆ’1)Â = 9081 275485 664660 641081 733027 601884 639581 589429 182549 516628 012836 432801 [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(7⁸⁹, 100, F₇, 62) (dual of [100, 11, 63]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁸⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 1387 645137 434620 170412 996794 367437 227294 662763 956098 087132 805083 834181 691479 [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(7⁹¹, 103, F₇, 63) (dual of [103, 12, 64]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound