MinT - Information on Result #1013199

Information on Result #1013199

Linear OOA(5⁵⁸, 1053, F₅, 3, 13) (dual of [(1053, 3), 3101, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5⁷, 10, F₅, 3, 6) (dual of [(10, 3), 23, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,23P) [i] based on function field F/F₅ with g(F) = 1 and N(F) ≥ 10, using
  - an explicitly constructive algebraic function field [i]
linear OOA(5⁵¹, 1043, F₅, 3, 13) (dual of [(1043, 3), 3078, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5⁵¹, 3129, F₅, 13) (dual of [3129, 3078, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁵¹, 3130, F₅, 13) (dual of [3130, 3079, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(5⁵¹, 3125, F₅, 13) (dual of [3125, 3074, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(5⁴⁶, 3125, F₅, 12) (dual of [3125, 3079, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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(5⁵⁸, 526, F₅, 15, 13) (dual of [(526, 15), 7832, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row