MinT - Information on Result #1013357

Information on Result #1013357

Linear OOA(5⁸³, 1059, F₅, 3, 18) (dual of [(1059, 3), 3094, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹², 16, F₅, 3, 9) (dual of [(16, 3), 36, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,38P) [i] based on function field F/F₅ with g(F) = 3 and N(F) ≥ 16, using
  - an explicitly constructive algebraic function field [i]
linear OOA(5⁷¹, 1043, F₅, 3, 18) (dual of [(1043, 3), 3058, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5⁷¹, 3129, F₅, 18) (dual of [3129, 3058, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁷¹, 3130, F₅, 18) (dual of [3130, 3059, 19]-code), using
    - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
      1. linear OA(5⁷¹, 3125, F₅, 18) (dual of [3125, 3054, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
      2. linear OA(5⁶⁶, 3125, F₅, 17) (dual of [3125, 3059, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(5⁰, 5, F₅, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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(5⁸³, 352, F₅, 21, 18) (dual of [(352, 21), 7309, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row