CAJ | 학술논문

该文利用有限环Fq+uFq 上循环自正交码，给出了一种构造有限域Fq上自正交码的方法。引入了Fq+uFq到Fqp的等距Gray映射，给出了Fq+uFq上循环自正交码存在的充分必要条件，证明了Fq+uFq 上长为n的循环自正交码的Gray象是Fq上长为pn的自正交码，由此构造了Fq上一些参数较好的自正交码。
해문이용유한배Fq+uFq 상순배자정교마，급출료일충구조유한역Fq상자정교마적방법。인입료Fq+uFq도Fqp적등거Gray영사，급출료Fq+uFq상순배자정교마존재적충분필요조건，증명료Fq+uFq 상장위n적순배자정교마적Gray상시Fq상장위pn적자정교마，유차구조료Fq상일사삼수교호적자정교마。
A method is proposed to construct self-orthogonal codes over the finite field Fq by using cyclic self-orthogonal codes over the finite ring q qF ?uF . A Gray map from q qF ?uF to pqF is introduced, and a sufficient and necessary condition for the existence of cyclic self-orthogonal codes over q qF ?uF is given. It is proved that the Gray image of a cyclic self-orthogonal code with length n over q qF ?uF is a self-orthogonal code with length pn over Fq . Further, some self-orthogonal codes over Fq with good parameters are constructed.