Geodesic
Locally Two-weight Property for Linear Codes and Its Application
Serdica Journal of Computing, Tome 17 (2024) no. 2, pp. 95-106.

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A q-ary linear code is an [n,k,d]q code, which is a linear code of length n, dimension k and minimum weight d over Fq, the field of order q. A fundamental problem in coding theory is to find nq(k,d), the minimum length n for which an [n,k,d]q code exists for given k,d and q. We introduce a new notion "e-locally 2-weight (mod q)" for linear codes over Fq and we give a necessary condition for the property. As an application, we prove the non-existence of some [n,4,d]9 codes with d ≡ −1 (mod 9), which determines n9(4,d) for some d.
Keywords: Linear Codes, Two-weight, Non-existence, Geometric Method 
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Kanda, Hitoshi; Kato, Atsuya; Maruta, Tatsuya. Locally Two-weight Property for Linear Codes and Its Application. Serdica Journal of Computing, Tome 17 (2024) no. 2, pp. 95-106. http://geodesic.mathdoc.fr/item/SJC_2024_17_2_a1/