Keita Ishizuka

Keita Ishizuka

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.

Keita Ishizuka

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.

Keita Ishizuka

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.

Keita Ishizuka, Yuhi Kamio

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.

Keita Ishizuka, Takashi Nose

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.