MinT - Information on Result #1302106

Information on Result #1302106

Linear OA(7⁶³, 74, F₇, 43) (dual of [74, 11, 44]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁶², 72, F₇, 43) (dual of [72, 10, 44]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(7⁵⁶, 64, F₇, 43) (dual of [64, 8, 44]-code), using
    - a quasi-cyclic or quasi-twisted code by Daskalov and Gulliver [i]
  2. linear OA(7⁵⁶, 66, F₇, 38) (dual of [66, 10, 39]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁵⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 153849 239853 628841 242167 040641 790977 948067 576327 [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(7⁶², 73, F₇, 42) (dual of [73, 11, 43]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁶²Â > V_b^sâˆ’1(kâˆ’1)Â = 22616 687553 150707 889439 370519 548700 591515 324837 260481 [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(7⁶⁴, 76, F₇, 43) (dual of [76, 12, 44]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound