MinT - Information on Result #941858

Information on Result #941858

Linear OOA(4¹⁷⁷, 92, F₄, 2, 133) (dual of [(92, 2), 7, 134]-NRT-code), using juxtaposition based on

linear OOA(4⁹, 8, F₄, 2, 8) (dual of [(8, 2), 7, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁹, 9, F₄, 2, 8) (dual of [(9, 2), 9, 9]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
linear OOA(4¹⁶¹, 84, F₄, 2, 124) (dual of [(84, 2), 7, 125]-NRT-code), using
- 1 step truncation [i] based on linear OOA(4¹⁶², 85, F₄, 2, 125) (dual of [(85, 2), 8, 126]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(16¹³, 17, F₁₆, 13) (dual of [17, 4, 14]-code or 17-arc in PG(12,16)), using
      - extended Reedâ€“Solomon code RS_e(4,16) [i]
      - the expurgated narrow-sense BCH-code C(I) with length 17Â | 16²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
    2. linear OOA(4⁸, 5, F₄, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;2,4) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁷⁷, 92, F₄, 2, 132) (dual of [(92, 2), 7, 133]-NRT-code)	[i]		Strength Reduction for OOAs