Ternary Linear Codes and Quadrics
Copyright policy )Ternary Linear Codes and Quadrics
For an $[n,k,d]_3$ code ${\cal C}$ with $gcd(d,3)=1$, we define a map $w_G$ from $\Sigma={\rm PG}(k-1,3)$ to the set of weights of codewords of ${\cal C}$ through a generator matrix $G$. A $t$-flat $\Pi$ in $\Sigma$ is called an $(i,j)_t$ flat if $(i,j)=(|\Pi \cap F_0|,|\Pi \cap F_1|)$, where $F_0 = \{P \in \Sigma | w_G(P) \equiv 0 \pmod{3}\}$, $F_1 = \{P \in \Sigma | w_G(P) \not\equiv 0,d \pmod{3}\}$. We give geometric characterizations of $(i,j)_t$ flats, which involve quadrics. As an application to the optimal linear codes problem, we prove the non-existence of a $[305,6,202]_3$ code, which is a new result.
Combinatorial structures in finite projective spaces, Combinatorial aspects of finite geometries, Geometric methods (including applications of algebraic geometry) applied to coding theory, Linear codes (general theory)
Combinatorial structures in finite projective spaces, Combinatorial aspects of finite geometries, Geometric methods (including applications of algebraic geometry) applied to coding theory, Linear codes (general theory)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).5 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!