MinT - Information on Result #909792

Information on Result #909792

Linear OOA(4²⁰¹, 103, F₄, 2, 154) (dual of [(103, 2), 5, 155]-NRT-code), using juxtaposition based on

linear OOA(4⁹¹, 48, F₄, 2, 71) (dual of [(48, 2), 5, 72]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4²⁰, 12, F₄, 2, 17) (dual of [(12, 2), 4, 18]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4²⁰, 14, F₄, 2, 17) (dual of [(14, 2), 8, 18]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,10P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(4²³, 12, F₄, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
    - dual of repetition NRT-code with length 12 [i]
  3. linear OOA(4²⁴, 12, F₄, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4²⁴, 12, F₄, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code) (see above)
linear OOA(4¹⁰⁵, 55, F₄, 2, 82) (dual of [(55, 2), 5, 83]-NRT-code), using
- 1 step truncation [i] based on linear OOA(4¹⁰⁶, 56, F₄, 2, 83) (dual of [(56, 2), 6, 84]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14 (see above)
    2. linear OOA(4²⁷, 14, F₄, 2, 27) (dual of [(14, 2), 1, 28]-NRT-code), using
      - dual of repetition NRT-code with length 14 [i]
    3. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code) (see above)

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(4²⁰¹, 103, F₄, 2, 153) (dual of [(103, 2), 5, 154]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²⁰¹, 103, F₄, 2, 152) (dual of [(103, 2), 5, 153]-NRT-code)	[i]		Strength Reduction for OOAs