MinT - Information on Result #1191758

Information on Result #1191758

Digital (44, 58, 1172)-net over F₈, using net defined by OOA based on linear OOA(8⁵⁸, 1172, F₈, 14, 14) (dual of [(1172, 14), 16350, 15]-NRT-code), using

OA 7-folding and stacking [i] based on linear OA(8⁵⁸, 8204, F₈, 14) (dual of [8204, 8146, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8⁵⁸, 8208, F₈, 14) (dual of [8208, 8150, 15]-code), using
  - trace code [i] based on linear OA(64²⁹, 4104, F₆₄, 14) (dual of [4104, 4075, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(10) [i] based on
      1. linear OA(64²⁷, 4096, F₆₄, 14) (dual of [4096, 4069, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      2. linear OA(64²¹, 4096, F₆₄, 11) (dual of [4096, 4075, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(64², 8, F₆₄, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,64)), using
        discarding factors / shortening the dual code based on linear OA(64², 64, F₆₄, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
        Reedâ€“Solomon code RS(62,64) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (45, 59, 1172)-net over F₈	[i]		Net Duplication