MinT - Information on Result #1302792

Information on Result #1302792

Linear OA(8¹¹⁹, 133, F₈, 85) (dual of [133, 14, 86]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(8¹¹⁸, 131, F₈, 85) (dual of [131, 13, 86]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(8¹⁰⁸, 118, F₈, 85) (dual of [118, 10, 86]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(8¹⁰⁷, 117, F₈, 85) (dual of [117, 10, 86]-code), using
      - a cyclic, quasi-cyclic, or quasi-twisted code by Daskalov, Hristov, and Metodieva [i]
  2. linear OA(8¹⁰⁸, 121, F₈, 77) (dual of [121, 13, 78]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8¹⁰⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 29 598844 364514 867321 458340 066672 413819 180331 811330 088996 843888 034962 848058 879134 613396 809184 651390 [i]
  3. linear OA(8⁷, 10, F₈, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,8)), using
    - Denniston code D(1,8) [i]
linear OA(8¹¹⁸, 132, F₈, 84) (dual of [132, 14, 85]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 8¹¹⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 31626 750897 705621 709077 053975 458873 690066 673635 167099 468770 496749 439822 260241 310969 590679 546803 810362 632064 [i]
linear OA(8⁰, 1, F₈, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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(8¹²⁰, 135, F₈, 85) (dual of [135, 15, 86]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound