2022/09/20 by Sam Adriaensen, Adriaensen, Sam, Simeon Ball +1 · 1 citation
Computer Science · #51E22 #94B05 #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #Error Correcting Code Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2209.09767
openalex publication_date 2022/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let C be an \mathbb Fq-linear (n,qhk,n-k+1)qh MDS code over \mathbb Fqh. If k=3, h ∈ \2,3\, n > max \qh-1,h q -1\ + 3, and C has three coordinates from which its projections are equivalent to linear codes, we prove that C itself is equivalent to a linear code. If k>3, n > q+k, and there are two disjoint subsets of coordinates whose combined size is at most k-2 from which the projections of C are equivalent to linear codes, we prove that C is equivalent to a code which is linear over a larger field than \mathbb Fq.