MinT - Information on Result #1302333

Information on Result #1302333

Linear OA(7¹⁰³, 115, F₇, 72) (dual of [115, 12, 73]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7¹⁰², 113, F₇, 72) (dual of [113, 11, 73]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(7¹⁰¹, 111, F₇, 72) (dual of [111, 10, 73]-code), using
    - constructionÂ X with VarÅ¡amov bound [i] based on
      1. linear OA(7⁹⁴, 102, F₇, 72) (dual of [102, 8, 73]-code), using
        2 times truncation [i] based on linear OA(7⁹⁶, 104, F₇, 74) (dual of [104, 8, 75]-code), using
        a quasi-cyclic or quasi-twisted code by Daskalov and Gulliver [i]
      2. linear OA(7⁹⁴, 104, F₇, 66) (dual of [104, 10, 67]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁹⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 12 012943 016506 011874 138400 036885 810792 912417 707372 380593 680481 590436 158668 101623 [i]
      3. linear OA(7⁵, 7, F₇, 5) (dual of [7, 2, 6]-code or 7-arc in PG(4,7)), using
        Reedâ€“Solomon code RS(2,7) [i]
  2. linear OA(7¹⁰¹, 112, F₇, 71) (dual of [112, 11, 72]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7¹⁰¹Â > V_b^sâˆ’1(kâˆ’1)Â = 17 908578 551853 613645 331215 940070 964950 622432 404320 095496 423447 921816 236854 735283 661623 [i]
  3. 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]
linear OA(7¹⁰², 114, F₇, 71) (dual of [114, 12, 72]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7¹⁰²Â > V_b^sâˆ’1(kâˆ’1)Â = 123 432082 132604 655156 053948 805317 992154 549202 708095 564745 309872 509541 918343 002945 996167 [i]
linear OA(7⁰, 1, F₇, 0) (dual of [1, 1, 1]-code) (see above)

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(7¹⁰⁴, 117, F₇, 72) (dual of [117, 13, 73]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound