MinT - Information on Result #1014251

Information on Result #1014251

Linear OOA(8³⁴, 2741, F₈, 3, 8) (dual of [(2741, 3), 8189, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁴, 9, F₈, 3, 4) (dual of [(9, 3), 23, 5]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;23,8) [i]
linear OOA(8³⁰, 2732, F₈, 3, 8) (dual of [(2732, 3), 8166, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8³⁰, 8196, F₈, 8) (dual of [8196, 8166, 9]-code), using
  - trace code [i] based on linear OA(64¹⁵, 4098, F₆₄, 8) (dual of [4098, 4083, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(64¹⁵, 4096, F₆₄, 8) (dual of [4096, 4081, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(64¹³, 4096, F₆₄, 7) (dual of [4096, 4083, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁵⁶, 5595143, F₈, 3, 16) (dual of [(5595143, 3), 16785273, 17]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(8¹⁶⁴, 5595143, F₈, 3, 17) (dual of [(5595143, 3), 16785265, 18]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs