MinT - Information on Result #2438328

Information on Result #2438328

Linear OOA(3²⁵⁰, 127, F₃, 2, 192) (dual of [(127, 2), 4, 193]-NRT-code), using strength reduction based on linear OOA(3²⁵⁰, 127, F₃, 2, 196) (dual of [(127, 2), 4, 197]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3⁴, 4, F₃, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;4,3) [i]
2. linear OOA(3²⁴², 123, F₃, 2, 191) (dual of [(123, 2), 4, 192]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(3⁴, 4, F₃, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code) (see above)
    2. linear OOA(3²³⁴, 119, F₃, 2, 186) (dual of [(119, 2), 4, 187]-NRT-code), using
      - 2 step truncation [i] based on linear OOA(3²³⁶, 120, F₃, 2, 188) (dual of [(120, 2), 4, 189]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(9²⁸, 30, F₉, 26) (dual of [30, 2, 27]-code), using
        repeating each code word 3 times [i] based on linear OA(9⁸, 10, F₉, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
        extended Reedâ€“Solomon code RS_e(2,9) [i]
        Simplex code S(2,9) [i]
        linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [i]

Mode: Constructive and 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 OOA(3²³⁸, 121, F₃, 2, 180) (dual of [(121, 2), 4, 181]-NRT-code)	[i]		Truncation for OOAs