MinT - Information on Result #1301542

Information on Result #1301542

Linear OA(5⁸⁶, 78162, F₅, 14) (dual of [78162, 78076, 15]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5⁸⁵, 78160, F₅, 14) (dual of [78160, 78075, 15]-code), using
- constructionÂ X applied to C_e(13) âŠ‚ C_e(8) [i] based on
  1. linear OA(5⁷⁸, 78125, F₅, 14) (dual of [78125, 78047, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
  2. linear OA(5⁵⁰, 78125, F₅, 9) (dual of [78125, 78075, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  3. linear OA(5⁷, 35, F₅, 4) (dual of [35, 28, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁷, 44, F₅, 4) (dual of [44, 37, 5]-code), using
      - codes constructed by inverting constructionÂ Y₁ [i]
linear OA(5⁸⁵, 78161, F₅, 13) (dual of [78161, 78076, 14]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5⁸⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 1819 061854 118118 608512 126373 306680 779295 246871 936393 513665 [i]
linear OA(5⁰, 1, F₅, 0) (dual of [1, 1, 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: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(5⁸⁶, 78162, F₅, 2, 14) (dual of [(78162, 2), 156238, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(5⁸⁶, 78162, F₅, 3, 14) (dual of [(78162, 3), 234400, 15]-NRT-code)	[i]
3	Digital (72, 86, 78162)-net over F₅	[i]
4	Linear OOA(5⁸⁶, 39081, F₅, 2, 14) (dual of [(39081, 2), 78076, 15]-NRT-code)	[i]	OOA Folding