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Keita Ishizuka

Publications and source records attributed to Keita Ishizuka.

13 recordsLinked to original sources
arXiv2026

Comparative monotonicity of linear codes by Hermitian and symplectic hull dimensions

Extending recent work on the Euclidean hull, we derive closed-form ratio decompositions for the number of linear codes with prescribed Hermitian and symplectic hull dimension. The Hermitian ratio admits a uniform lower bound of at least $2/3$, while the symplectic ratio decays to $1/q^2$ asymptotically; a comparative analysis traces this qualitative difference to the Witt classification of the corresponding classical groups. The results translate directly into monotonicity statements for the number of entanglement-assisted quantum codes obtainable from Hermitian-hull-graded $[n, k]_{q^2}$ and symplectic-hull-graded $[2n, k]_q$ classical codes via the Guenda-Jitman-Gulliver and Wilde-Brun constructions, respectively.

math.CO↗
arXiv2026

Almost All Vectorial Functions Have Trivial Extended-Affine Stabilizers

We prove that asymptotically almost all vectorial functions over finite fields have trivial extended-affine stabilizers. As a consequence, the number of EA-equivalence classes is asymptotically equal to the naive estimate, namely the total number of functions divided by the size of the EA-group, with vanishing relative error. Furthermore, we derive upper bounds on collision probabilities for both extended-affine and CCZ equivalences. For EA-equivalence, we leverage the trivial-stabilizer result to establish a matching lower bound, yielding a tight asymptotic formula that shows two independently sampled functions are EA-equivalent with super-exponentially small probability. The results validate random sampling strategies for cryptographic primitive design and show that functions with nontrivial EA-stabilizers form an exponentially rare subset.

math.CO↗
arXiv2026

The Closure of LCD-to-GI Reductions via Generalized Inner Products

The Permutation Equivalence Problem (PEP) for linear codes is a fundamental problem in coding theory and cryptography. A recent reduction shows that PEP for Linear Complementary Dual (LCD) codes reduces to Graph Isomorphism (GI) via orthogonal projectors, but is restricted to codes with trivial hull. We prove that this approach extends to bilinear forms $M = aI + bJ$, and that no other nondegenerate symmetric form yields a valid reduction. A code is reducible if and only if its hull dimension is at most $1$ with an explicit condition on the hull vector; in characteristic $2$, only LCD codes are reducible. This establishes the closure of the orthogonal projector method. We derive exact enumeration formulas via character sums over quadratic forms and provide a polynomial-time reduction algorithm.

cs.IT↗
arXiv2026

Binary LCD Codes and Their Graph Representations

We give a complete characterization of simple graphs whose adjacency matrices generate binary linear complementary dual (LCD) codes. In particular, we completely characterize a distance-regular graph which yields an LCD code in terms of the intersection array parameters. This necessary and sufficient criterion strengthens the previously known sufficient conditions and unifies the cases of complete, Hamming, Johnson, and Grassmann graphs. As further applications, we prove that non-isomorphic conference graphs with $q \equiv 1 \pmod 8$ yield inequivalent codes and we classify all simple graphs with idempotent adjacency matrices on at most $13$ vertices via mass formulas for binary LCD codes.

math.CO↗
arXiv2026

Binary Caps and LCD Codes with Large Dimensions

We establish a connection between linear complementary dual (LCD) codes and caps in projective space. Using this framework and the structure theory of maximal caps, we derive nonexistence theorems for LCD codes with minimum distance at least $4$, providing computation-free proofs that were previously obtained only through exhaustive search. As an application, we completely determine the optimal minimum distances for codimensions $7$ and $8$ for the first time.

cs.IT↗
arXiv2024

Constructions of self-orthogonal and LCD subspace codes

Recently, the notions of self-orthogonal subspace codes and LCD subspace codes were introduced, and LCD subspace codes obtained from mutually unbiased weighing matrices were studied. In this paper, we provide a method of constructing self-orthogonal and LCD subspace codes from a set of matrices under certain conditions. In particular, we give constructions of self-orthogonal and LCD subspace codes from mutually quasi-unbiased weighing matrices, linked systems of symmetric designs, and linked systems of symmetric group divisible designs, Deza graphs and their equitable partitions.

math.CO↗
arXiv2023

Ternary extremal four-negacirculant self-dual codes

In this note, we give basic properties of ternary four-negacirculant self-dual codes. By exhaustive computer search based on the properties, we complete a classification of ternary extremal four-negacirculant self-dual codes of lengths 40, 44, 48, 52 and 60.

math.CO↗
arXiv2022

Construction of quaternary Hermitian LCD codes

We introduce a general construction of many Hermitian LCD $[n, k]$ codes from a given Hermitian LCD $[n, k]$ code. Furthermore, we present some results on punctured codes and shortened codes of quaternary Hermitian LCD codes. As an application, we improve some of the previously known lower bounds on the largest minimum weights of quaternary Hermitian LCD codes of length $12 \le n \le 30$.

cs.IT↗
arXiv2021

Construction for both self-dual codes and LCD codes

From a given $[n, k]$ code $C$, we give a method for constructing many $[n, k]$ codes $C'$ such that the hull dimensions of $C$ and $C'$ are identical. This method can be applied to constructions of both self-dual codes and linear complementary dual codes (LCD codes for short). Using the method, we construct 661 new inequivalent extremal doubly even $[56, 28, 12]$ codes. Furthermore, constructing LCD codes by the method, we improve some of the previously known lower bounds on the largest minimum weights of binary LCD codes of length $n=26,28 \le n \le 40$.

cs.IT↗
arXiv2021

On the existence of quaternary Hermitian LCD codes with Hermitian dual distance $1$

For $k \ge 2$ and a positive integer $d_0$, we show that if there exists no quaternary Hermitian linear complementary dual $[n,k,d]$ code with $d \ge d_0$ and Hermitian dual distance greater than or equal to $2$, then there exists no quaternary Hermitian linear complementary dual $[n,k,d]$ code with $d \ge d_0$ and Hermitian dual distance $1$. As a consequence, we generalize a result by Araya, Harada and Saito on the nonexistence of some quaternary Hermitian linear complementary dual codes.

cs.IT↗
arXiv2020

Classification of optimal quaternary Hermitian LCD codes of dimension $2$

Hermitian linear complementary dual codes are linear codes whose intersection with their Hermitian dual code is trivial. The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension $2$ is known for each length. We give the complete classification of optimal quaternary Hermitian linear complementary dual codes of dimension $2$.

math.CO↗
arXiv2019

Developing a Multi-Platform Speech Recording System Toward Open Service of Building Large-Scale Speech Corpora

This paper briefly reports our ongoing attempt at the development of a multi-platform browser-based speech recording system. We designed the system toward a service of providing open service of building large-scale speech corpora at a low-cost for any researchers and developers related to speech processing. The recent increase in the use of crowdsourcing services, e.g., Amazon Mechanical Turk, enable us to reduce the cost of collecting speakers in the web, and there have been many attempts to develop the automated speech collecting platforms or application that is designed for the use the crowdsourcing. However, one of the major problems in the previous studies and developments for the attempts is that most of the systems are not a form of common service of speech recording and corpus building, and each corpus builder is necessary to develop the system in their own environment including a web server. For this problem, we develope a new platform where both the corpus builders and recording participants can commonly use a single system and service by creating their user accounts. A brief introduction of the system is given in this paper as the start of this challenge.

cs.HC↗