Codes Associated with Nondegenerate Quadrics of a Symplectic Space of Even Order

✍ Scribed by N.S Narasimha Sastry; Peter Sin

• Book ID: 102586050
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 140 KB
• Volume: 94
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.2000.3118

✦ Synopsis

This paper studies the incidence relation between the points and quadrics in the projective space of a symplectic vector space over a field of even order. The 2-rank of the incidence matrix is determined. This is achieved by viewing the code generated by incidence vectors as a module for the symplectic group and applying the 2-modular representation theory of this group. The radical series of this module is also described.