MinT - Information on Result #2638950

Information on Result #2638950

Linear OOA(4²⁵⁸, 87, F₄, 3, 228) (dual of [(87, 3), 3, 229]-NRT-code), using strength reduction based on linear OOA(4²⁵⁸, 87, F₄, 3, 229) (dual of [(87, 3), 3, 230]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4⁶, 3, F₄, 3, 6) (dual of [(3, 3), 3, 7]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁶, 4, F₄, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;6,4) [i]
2. linear OOA(4²⁴⁹, 84, F₄, 3, 222) (dual of [(84, 3), 3, 223]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4⁶, 3, F₄, 3, 6) (dual of [(3, 3), 3, 7]-NRT-code) (see above)
    2. linear OOA(4²⁴⁰, 81, F₄, 3, 215) (dual of [(81, 3), 3, 216]-NRT-code), using
      - repeating each code word 9 times [i] based on linear OOA(4²⁴, 9, F₄, 3, 23) (dual of [(9, 3), 3, 24]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,3P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [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(4²⁵⁶, 86, F₄, 3, 226) (dual of [(86, 3), 2, 227]-NRT-code)	[i]		Truncation for OOAs