MinT - Information on Result #1303486

Information on Result #1303486

Linear OA(9¹²⁸, 142, F₉, 94) (dual of [142, 14, 95]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(9¹²⁷, 140, F₉, 94) (dual of [140, 13, 95]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(9¹²⁶, 138, F₉, 94) (dual of [138, 12, 95]-code), using
    - constructionÂ X with VarÅ¡amov bound [i] based on
      1. linear OA(9¹²⁰, 130, F₉, 94) (dual of [130, 10, 95]-code), using
        a cyclic, quasi-cyclic, or quasi-twisted code by Daskalov, Hristov, and Metodieva [i]
      2. linear OA(9¹²⁰, 132, F₉, 89) (dual of [132, 12, 90]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9¹²⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 2 977359 887864 425054 166970 017342 940468 049101 576330 089018 208333 422789 306281 120181 971609 119189 244060 434565 444271 527641 [i]
      3. linear OA(9⁴, 6, F₉, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,9)), using
        discarding factors / shortening the dual code based on linear OA(9⁴, 9, F₉, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,9)), using
        Reedâ€“Solomon code RS(5,9) [i]
  2. linear OA(9¹²⁶, 139, F₉, 93) (dual of [139, 13, 94]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9¹²⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 1 619577 125166 516271 583078 109966 851054 292261 733968 188875 138349 128202 891161 048544 695265 447523 772782 181558 212401 571771 862929 [i]
  3. linear OA(9⁰, 1, F₉, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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(9¹²⁷, 141, F₉, 93) (dual of [141, 14, 94]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9¹²⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 13 793423 733107 618104 474616 602730 864941 981722 368236 376583 124200 561123 282022 039268 931654 690741 373814 639767 806052 148395 060449 [i]
linear OA(9⁰, 1, F₉, 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(9¹²⁹, 144, F₉, 94) (dual of [144, 15, 95]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound