arXiv subjects

Padmapani Seneviratne

Publications and source records attributed to Padmapani Seneviratne.

5 recordsLinked to original sources

arXiv2026

Permutation decoding of algebraic geometry codes from Hermitian and norm-trace curves

Permutation decoding is a process that utilizes the permutation automorphism group of a linear code to correct errors in received words. Given a received word, a set of automorphisms, called a PD set, moves errors out of the information positions so that the original message can be determined. In this paper, we investigate permutation decoding for certain families of algebraic geometry codes. Automorphisms of the underlying curve are used to specify permutation automorphisms of the code. Specifically, we describe permutation decoding sets that correct specific burst errors for one-point codes on Hermitian and norm-trace curves.

cs.IT↗

arXiv2023

New Qutrit Codes from Pure and Bordered Multidimensional Circulant Construction

We use multidimensional circulant approach to construct new qutrit stabilizer $\dsb{\ell, 0, d}$ codes with parameters $(\ell, d) \in \{(51, 16), (52, 16), (54, 17), (55, 17), (57, 17)\}$ through symplectic self-dual additive codes over $\F_9$. In addition to these five new codes, we use bordered construction to derive two more qutrit codes with parameters $(\ell, d) \in \{(53, 16), (56, 17)\}$ that improve upon previously best known parameters.

cs.IT↗

arXiv2023

New Qubit Codes from Multidimensional Circulant Graphs

Two new qubit stabilizer codes with parameters $[77, 0, 19]_2$ and $[90, 0, 22]_2$ are constructed for the first time by employing additive symplectic self-dual $\F_4$ codes from multidimensional circulant (MDC) graphs. We completely classify MDC graph codes for lengths $4\le n \le 40$ and show that many optimal $\dsb{\ell, 0, d}$ qubit codes can be obtained from the MDC construction. Moreover, we prove that adjacency matrices of MDC graphs have nested block circulant structure and determine isomorphism properties of MDC graphs.

cs.IT↗

arXiv2021

Two New Zero-Dimensional Qubit Codes from Bordered Metacirculant Construction

We construct qubit stabilizer codes with parameters $[[81, 0, 20]]$ and $[[94, 0, 22]]$ for the first time. We use symplectic self-dual additive codes over $\mathbb{F}_4$ built by modifying the adjacency matrices of suitable metacirculant graphs found by a randomized search procedure.

cs.IT↗

arXiv2021

Improved Quantum Codes from Metacirculant Graphs via Self-Dual Additive $\mathbb{F}_4$-Codes

We use symplectic self-dual additive codes over $\mathbb{F}_4$ obtained from metacirculant graphs to construct, for the first time, $[[\ell, 0, d ]]$ qubit codes with parameters $(\ell,d) \in \{(78, 20), (90, 21), (91, 22), (93,21),(96,21)\}$. Secondary constructions applied to the qubit codes result in many qubit codes that perform better than the previous best-known.

cs.IT↗