MinT - Information on Result #2768359

Information on Result #2768359

Linear OOA(2²⁶⁰, 67, F₂, 4, 188) (dual of [(67, 4), 8, 189]-NRT-code), using strength reduction based on linear OOA(2²⁶⁰, 67, F₂, 4, 192) (dual of [(67, 4), 8, 193]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2²⁴, 8, F₂, 4, 20) (dual of [(8, 4), 8, 21]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,11P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2²²⁸, 59, F₂, 4, 171) (dual of [(59, 4), 8, 172]-NRT-code), using
  - 4 step truncation [i] based on linear OOA(2²³², 60, F₂, 4, 175) (dual of [(60, 4), 8, 176]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(16¹⁰, 12, F₁₆, 10) (dual of [12, 2, 11]-code or 12-arc in PG(9,16)), using
        discarding factors / shortening the dual code based on linear OA(16¹⁰, 16, F₁₆, 10) (dual of [16, 6, 11]-code or 16-arc in PG(9,16)), using
        Reedâ€“Solomon code RS(6,16) [i]
      2. linear OOA(2¹⁶, 5, F₂, 4, 15) (dual of [(5, 4), 4, 16]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [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(2²⁵⁷, 66, F₂, 4, 185) (dual of [(66, 4), 7, 186]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁵⁶, 66, F₂, 4, 184) (dual of [(66, 4), 8, 185]-NRT-code)	[i]
3	Linear OOA(2²⁵³, 65, F₂, 4, 181) (dual of [(65, 4), 7, 182]-NRT-code)	[i]