MinT - Information on Result #1302297

Information on Result #1302297

Linear OA(7⁹⁹, 111, F₇, 69) (dual of [111, 12, 70]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁹⁸, 109, F₇, 69) (dual of [109, 11, 70]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(7⁹⁷, 107, F₇, 69) (dual of [107, 10, 70]-code), using
    - constructionÂ X with VarÅ¡amov bound [i] based on
      1. linear OA(7⁹¹, 99, F₇, 69) (dual of [99, 8, 70]-code), using
        5 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(7⁹¹, 101, F₇, 64) (dual of [101, 10, 65]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁹¹Â > V_b^sâˆ’1(kâˆ’1)Â = 49608 740193 239979 659869 638434 093683 220025 461284 980333 428817 239218 461116 865121 [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]
  2. linear OA(7⁹⁷, 108, F₇, 68) (dual of [108, 11, 69]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁹⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 7710 561682 606532 268693 525707 079832 088789 026599 270545 374902 302041 537023 688695 743383 [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(7⁹⁸, 110, F₇, 68) (dual of [110, 12, 69]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁹⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 51846 562896 749187 166600 477794 863983 031503 895875 770524 514677 258053 750812 527757 012967 [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(7¹⁰⁰, 113, F₇, 69) (dual of [113, 13, 70]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound