MinT - Information on Result #1183613

Information on Result #1183613

Linear OOA(3²⁰¹, 6710991, F₃, 15, 11) (dual of [(6710991, 15), 100664664, 12]-NRT-code), using OOA stacking with additional row based on linear OOA(3²⁰¹, 6710992, F₃, 5, 11) (dual of [(6710992, 5), 33554759, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁴⁶, 3355496, F₃, 5, 5) (dual of [(3355496, 5), 16777434, 6]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁴⁶, 4194301, F₃, 5, 5) (dual of [(4194301, 5), 20971459, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(3⁴⁶, large, F₃, 5) (dual of [large, large−46, 6]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
2. linear OOA(3¹⁵⁵, 3355496, F₃, 5, 11) (dual of [(3355496, 5), 16777325, 12]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(3⁶, 56, F₃, 5, 3) (dual of [(56, 5), 274, 4]-NRT-code), using
      - appending 2 arbitrary columns [i] based on linear OOA(3⁶, 56, F₃, 3, 3) (dual of [(56, 3), 162, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(3⁶, 56, F₃, 2, 3) (dual of [(56, 2), 106, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
        the Hill cap [i]
    2. linear OOA(3⁴³, 1677720, F₃, 5, 5) (dual of [(1677720, 5), 8388557, 6]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3⁴³, 2391491, F₃, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(3⁴³, 4782983, F₃, 5) (dual of [4782983, 4782940, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(3⁴³, 4782969, F₃, 5) (dual of [4782969, 4782926, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(3²⁹, 4782969, F₃, 4) (dual of [4782969, 4782940, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(3⁰, 14, F₃, 0) (dual of [14, 14, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
    3. 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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (190, 201, 6710991)-net over F₃	[i]		Net Defined by OOA