MinT - Information on Result #1027760

Information on Result #1027760

Linear OOA(8¹⁷¹, 58, F₈, 3, 159) (dual of [(58, 3), 3, 160]-NRT-code), using juxtaposition based on

linear OOA(8⁶, 3, F₈, 3, 6) (dual of [(3, 3), 3, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁶, 8, F₈, 3, 6) (dual of [(8, 3), 18, 7]-NRT-code), using
  - Reedâ€“Solomon NRT-code RS(3;18,8) [i]
linear OOA(8¹⁶², 55, F₈, 3, 152) (dual of [(55, 3), 3, 153]-NRT-code), using
- 6 step truncation [i] based on linear OOA(8¹⁶⁸, 57, F₈, 3, 158) (dual of [(57, 3), 3, 159]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(8²⁴, 9, F₈, 3, 24) (dual of [(9, 3), 3, 25]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(3;3,8) [i]
    2. linear OOA(8¹⁴¹, 48, F₈, 3, 133) (dual of [(48, 3), 3, 134]-NRT-code), using
      - repeating each code word 2 times [i] based on linear OOA(8⁶⁹, 24, F₈, 3, 66) (dual of [(24, 3), 3, 67]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,5P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
        the Klein quartic over F₈ [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁷¹, 58, F₈, 3, 158) (dual of [(58, 3), 3, 159]-NRT-code)	[i]		Strength Reduction for OOAs