8 papers
A New Approach to Code Smoothing Bounds
Tsuyoshi Miezaki, Yusaku Nishimura, Katsuyuki Takashima
Code smoothing is a phenomenon in which an error distribution makes a code statistically close to the uniform distribution over the ambient space. This closeness is measured by the…
Fibonacci and Lucas numbers arising from two-component spanning forests of wheel graphs
Tsuyoshi Miezaki, Shunya Tamura
In this paper, we present a constructive bijection between a conditioned spanning forest of the wheel graph and a spanning tree of the fan graph . In addition, by ap…
Higher and extended Jacobi polynomials for codes
Himadri Shekhar Chakraborty, Tsuyoshi Miezaki
In this paper, we introduce Jacobi polynomial generalizations of several classical invariants in coding theory over finite fields, specifically, the higher and extended weight enum…
On Lattice Isomorphism Problems for Lattices from LCD Codes over Finite Rings
Yusaku Nishimura, Katsuyuki Takashima, Tsuyoshi Miezaki
These days, post-quantum cryptography based on the lattice isomorphism problem has been proposed. Ducas-Gibbons introduced the hull attack, which solves the lattice isomorphism pro…
Neighbors, neighbor graphs and invariant rings in coding theory
Himadri Shekhar Chakraborty, Williams Chiari, Tsuyoshi Miezaki +1
In the present paper, we discuss the class of Type III and Type IV codes from the perspectives of neighbors. Our investigation analogously extends the results originally presented…
Jacobi polynomials, invariant rings, and generalized -designs
Himadri Shekhar Chakraborty, Nur Hamid, Tsuyoshi Miezaki +1
In the present paper, we provide results that relate the Jacobi polynomials in genus . We show that if a code is -homogeneous that is, the codewords of the code for every giv…
Harmonic higher and extended weight enumerators
Thomas Britz, Himadri Shekhar Chakraborty, Tsuyoshi Miezaki
In this paper, we present the harmonic generalizations of well-known polynomials of codes over finite fields, namely the higher weight enumerators and the extended weight enumerato…
A criterion for determining whether multiple shells support a -design
Madoka Awada, Reina Ishikawa, Tsuyoshi Miezaki +1
In this paper, we provide a criterion for determining whether multiple shells support a -design. We construct as a corollary an infinite series of -designs using power residu…