The Subfield Codes of Ovoid Codes

被引：30

作者：

Ding, Cunsheng ^{[1
]}

Heng, Ziling ^{[2
]}

机构：

[1] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Hong Kong, Peoples R China

[2] Changan Univ, Sch Sci, Xian 710064, Shaanxi, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2019年 / 65卷 / 08期

关键词：

Elliptic quadric; linear code; weight distribution; ovoid;

D O I：

10.1109/TIT.2019.2907276

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Ovoids in PG(3, GF(q)) have been an interesting topic in coding theory, combinatorics, and finite geometry for a long time. So far only two families of ovoids are known. The first is the elliptic quadrics and the second is the Tits ovoids. It is known that an ovoid in PG(3, GF(q)) corresponds to a [q(2) + 1, 4, q(2) -q] code over GF(q), which is called an ovoid code. The objectives of this paper are to develop the general theories of subfield codes and to study the subfield codes of the two families of ovoid codes. The dimensions, minimum weights, and the weight distributions of the subfield codes of the elliptic quadric codes and Tits ovoid codes are settled. The parameters of the duals of these subfield codes are also studied. Some of the codes presented in this paper are optimal, and some are distance-optimal. The parameters of the subfield codes are new.

引用

页码：4715 / 4729

页数：15

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