MinT - Information on Result #2438324

Information on Result #2438324

Linear OOA(3²⁵⁰, 127, F₃, 2, 197) (dual of [(127, 2), 4, 198]-NRT-code), using strength reduction based on linear OOA(3²⁵⁰, 127, F₃, 2, 198) (dual of [(127, 2), 4, 199]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3¹⁰, 7, F₃, 2, 9) (dual of [(7, 2), 4, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3²³⁶, 120, F₃, 2, 188) (dual of [(120, 2), 4, 189]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. 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]
    2. 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		Method
1	Linear OOA(3²³⁸, 121, F₃, 2, 185) (dual of [(121, 2), 4, 186]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(3²³⁴, 119, F₃, 2, 181) (dual of [(119, 2), 4, 182]-NRT-code)	[i]
3	Linear OOA(3²³², 118, F₃, 2, 179) (dual of [(118, 2), 4, 180]-NRT-code)	[i]
4	Linear OOA(3²³⁰, 117, F₃, 2, 177) (dual of [(117, 2), 4, 178]-NRT-code)	[i]
5	Linear OOA(3²²⁶, 115, F₃, 2, 173) (dual of [(115, 2), 4, 174]-NRT-code)	[i]
6	Linear OOA(3²²⁴, 114, F₃, 2, 171) (dual of [(114, 2), 4, 172]-NRT-code)	[i]
7	Linear OOA(3²²², 113, F₃, 2, 169) (dual of [(113, 2), 4, 170]-NRT-code)	[i]