MinT - Information on Result #1117205

Information on Result #1117205

Linear OOA(3¹³⁶, 1690685, F₃, 5, 11) (dual of [(1690685, 5), 8453289, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3³⁰, 12965, F₃, 5, 5) (dual of [(12965, 5), 64795, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(3³⁰, 12966, F₃, 2, 5) (dual of [(12966, 2), 25902, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3², 4, F₃, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;6,3) [i]
    2. linear OOA(3²⁸, 12962, F₃, 2, 5) (dual of [(12962, 2), 25896, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(3²⁸, 25924, F₃, 5) (dual of [25924, 25896, 6]-code), using
        trace code [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(3¹⁰⁶, 1677720, F₃, 5, 11) (dual of [(1677720, 5), 8388494, 12]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3¹⁰⁶, 8388600, F₃, 11) (dual of [8388600, 8388494, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰⁶, large, F₃, 11) (dual of [large, large−106, 12]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹³⁶, 1690684, F₃, 15, 11) (dual of [(1690684, 15), 25360124, 12]-NRT-code)	[i]		OOA Stacking with Additional Row