Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurrin...Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurring sequences and subfield subcodes. Let Mqm(f(x)) denote the set of all linear recurring sequences over Fqm with characteristic polynomial f(x) over Fqm . Denote the restriction of Mqm(f(x)) to sequences over Fq and the set after applying trace function to each sequence in Mqm(f(x)) by Mqm(f(x)) | Fq and Tr( Mqm(f(x))), respectively. It is shown that these two sets are both complete sets of linear recurring sequences over Fq with some characteristic polynomials over Fq. In this paper, we firstly determine the characteristic polynomials for these two sets. Then, using these results, we determine the generator polynomials of subfield subcodes and trace codes of cyclic codes over Fqm .展开更多
Most salmonid taxa have an anadromous life history strategy, whereby fish migrate to saltwater habitats for a growth period before returning to freshwater habitats for spawning. Moreover, several species are character...Most salmonid taxa have an anadromous life history strategy, whereby fish migrate to saltwater habitats for a growth period before returning to freshwater habitats for spawning. Moreover, several species are characterized by different life history tactics whereby resident and anadromous forms may occur in genetically differentiated populations within a same species, as well as polymorphism within a population. The molecular mechanisms underlying the physiological differences between anadromous and resident forms during the first transition from freshwater to saltwater environments are only partially understood. Insofar re- search has typically focused on species of the genus Salmo. Here, using a 16,000 cDNA array, we tested the hypothesis that ana- dromous brook charr Salvelinus fontinalis are characterized by differences in their transcriptome relative to resident brook charr before the anadromous fish migration. Families originating from parapatric populations of anadromous and resident charr were reared in controlled environments mimicking natural temperature and photoperiod, and sampled in spring, while still in fresh wa- ter. While anadromous and resident charr showed similar transcriptome profiles in white muscle, they were characterized by striking differences in their gill transcriptome profiles. Genes that were upregulated in the gills of anadromous charr were princi- pally involved in metabolism （mitochondrial electron transport chain, glucose metabolism, and protein synthesis）, development （tissue differentiation） and innate immunity. We discuss the nature of these transcriptomic differences in relation to molecular mechanisms underlying the expression of anadromous and resident life history tactics and suggest that the anadromous charr express some of the molecular processes present in other migratory salmonids [Current Zoology 58 （1）： 158-170, 2012].展开更多
基金supported by National Key Basic Research Program of China(973 Program)(Grant No.2013CB834204)National Natural Science Foundation of China(Grant Nos.61171082 and 10990011)
文摘Linear recurring sequences over finite fields play an important role in coding theory and cryptography. It is known that subfield subcodes of linear codes yield some good codes. In this paper, we study linear recurring sequences and subfield subcodes. Let Mqm(f(x)) denote the set of all linear recurring sequences over Fqm with characteristic polynomial f(x) over Fqm . Denote the restriction of Mqm(f(x)) to sequences over Fq and the set after applying trace function to each sequence in Mqm(f(x)) by Mqm(f(x)) | Fq and Tr( Mqm(f(x))), respectively. It is shown that these two sets are both complete sets of linear recurring sequences over Fq with some characteristic polynomials over Fq. In this paper, we firstly determine the characteristic polynomials for these two sets. Then, using these results, we determine the generator polynomials of subfield subcodes and trace codes of cyclic codes over Fqm .
文摘Most salmonid taxa have an anadromous life history strategy, whereby fish migrate to saltwater habitats for a growth period before returning to freshwater habitats for spawning. Moreover, several species are characterized by different life history tactics whereby resident and anadromous forms may occur in genetically differentiated populations within a same species, as well as polymorphism within a population. The molecular mechanisms underlying the physiological differences between anadromous and resident forms during the first transition from freshwater to saltwater environments are only partially understood. Insofar re- search has typically focused on species of the genus Salmo. Here, using a 16,000 cDNA array, we tested the hypothesis that ana- dromous brook charr Salvelinus fontinalis are characterized by differences in their transcriptome relative to resident brook charr before the anadromous fish migration. Families originating from parapatric populations of anadromous and resident charr were reared in controlled environments mimicking natural temperature and photoperiod, and sampled in spring, while still in fresh wa- ter. While anadromous and resident charr showed similar transcriptome profiles in white muscle, they were characterized by striking differences in their gill transcriptome profiles. Genes that were upregulated in the gills of anadromous charr were princi- pally involved in metabolism （mitochondrial electron transport chain, glucose metabolism, and protein synthesis）, development （tissue differentiation） and innate immunity. We discuss the nature of these transcriptomic differences in relation to molecular mechanisms underlying the expression of anadromous and resident life history tactics and suggest that the anadromous charr express some of the molecular processes present in other migratory salmonids [Current Zoology 58 （1）： 158-170, 2012].
