MinT - Information on Result #1302349

Information on Result #1302349

Linear OA(7¹⁰⁶, 117, F₇, 75) (dual of [117, 11, 76]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7¹⁰⁵, 115, F₇, 75) (dual of [115, 10, 76]-code), using
- concatenation of two codes [i] based on
  1. linear OA(49¹⁸, 23, F₄₉, 18) (dual of [23, 5, 19]-code or 23-arc in PG(17,49)), using
    - discarding factors / shortening the dual code based on linear OA(49¹⁸, 49, F₄₉, 18) (dual of [49, 31, 19]-code or 49-arc in PG(17,49)), using
      - Reedâ€“Solomon code RS(31,49) [i]
  2. linear OA(7³, 5, F₇, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,7) or 5-cap in PG(2,7)), using
    - discarding factors / shortening the dual code based on linear OA(7³, 7, F₇, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
      - Reedâ€“Solomon code RS(4,7) [i]
linear OA(7¹⁰⁵, 116, F₇, 74) (dual of [116, 11, 75]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7¹⁰⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 41240 268919 487309 506865 072492 974130 955992 077399 380303 262775 849735 602400 833399 019546 398423 [i]
linear OA(7⁰, 1, F₇, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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		This result only	Method
1	Linear OA(7¹⁰⁷, 119, F₇, 75) (dual of [119, 12, 76]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound