
629 F.3d 1219 (2011)
Ricardo GONZALEZ, Petitioner-Appellant,
v.
SECRETARY, FLORIDA DEPARTMENT OF CORRECTIONS, Respondent-Appellee.
No. 09-15599.
United States Court of Appeals, Eleventh Circuit.
January 3, 2011.
*1220 Todd Gerald Scher (Court-Appointed), Sp. Asst. CCRC-South, Miami Beach, FL, for Gonzalez.
Sandra Sue Jaggard, Miami, FL, for Respondent-Appellee.
Before EDMONDSON, BARKETT and PRYOR, Circuit Judges.
PER CURIAM:
Ricardo Gonzalez, a Florida prisoner on death row, appeals from the district court's denial of his petition for a writ of habeas corpus, brought pursuant to 28 U.S.C. § 2254. In 1994, a jury found Gonzalez guilty of first-degree murder of a law enforcement officer and lesser offenses in connection with an armed bank robbery. The Florida Supreme Court affirmed Gonzalez's convictions on direct appeal, but vacated his death sentence and remanded for a new sentencing hearing. Gonzalez v. State, 700 So.2d 1217 (Fla.1997) ("Gonzalez I"), cert. denied, Gonzalez v. Florida, 523 U.S. 1062, 118 S.Ct. 1393, 140 L.Ed.2d 652 (1998). On remand, the trial court reimposed the death penalty, and the Florida Supreme Court affirmed. Gonzalez v. State, 786 So.2d 559 (Fla.2001).
Twenty days before the one-year federal habeas statute of limitations was set to expire, see 28 U.S.C. § 2244(d)(1), Gonzalez filed an incomplete "shell" motion for post-conviction relief in state court, pursuant to Fla. R.Crim. P. 3.850. Gonzalez acknowledged that he filed this motion in order to toll the federal limitations period under 28 U.S.C. § 2244(d)(2). Although the trial court struck the "shell" motion, the Florida Supreme Court granted Gonzalez leave to amend, and he subsequently filed an amended Rule 3.850 motion after the expiration of the federal limitations period. The trial court ultimately denied Gonzalez's amended motion on the merits, and the Florida Supreme Court affirmed. Gonzalez v. State, 990 So.2d 1017 (Fla. 2008).
Shortly thereafter, Gonzalez filed the instant federal habeas petition. The district court denied the petition, but granted a certificate of appealability on three issues: 1) whether Gonzalez's federal habeas petition was timely; 2) whether the admission of Gonzalez's co-defendants' confessions at his trial was harmful with respect to his guilt; and 3) whether the trial court erroneously denied two of his peremptory challenges. Upon review of the record and the parties' briefs, and having the benefit of oral argument, we affirm the district court's denial of Gonzalez's federal habeas petition.
"When examining a district court's denial of a § 2254 habeas petition, we review questions of law and mixed questions of law and fact de novo, and findings of fact for clear error." Rhode v. Hall, 582 F.3d 1273, 1279 (11th Cir.2009) (citation omitted), cert. denied, ___ U.S. ___, 130 S.Ct. 3399, 177 L.Ed.2d 313 (2010). Under the Antiterrorism and Effective Death Penalty Act ("AEDPA"), we may grant habeas relief to a state prisoner on any claim adjudicated on the merits in state court if that adjudication "resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States ...." 28 U.S.C. § 2254(d)(1).
*1221 The first issue of whether Gonzalez's federal habeas petition was timely turns on whether his "shell" motion was "properly filed" so as to toll the federal limitations period under § 2244(d)(2). Gonzalez argues that, although his "shell" motion was stricken by the trial court, his amended Rule 3.850 motion was deemed to have "related back" and thus rendered his "shell" motion "properly filed." Gonzalez relies on Gore v. State, where the Florida Supreme Court indicated that the relation back doctrine rendered an initially-stricken state post-conviction motion "properly filed" under Florida law for purposes of § 2244(d)(2). 24 So.3d 1, 15-16 (Fla.2009). The state responds that this argument is foreclosed by our case law. See Melson v. Allen, 548 F.3d 993, 998 (11th Cir.2008), vacated on other grounds, ___ U.S. ___, 130 S.Ct. 3491, 177 L.Ed.2d 1081 (2010); Sibley v. Culliver, 377 F.3d 1196, 1204 (11th Cir.2004). Gonzalez suggests that our cases are inapplicable because none of them involved a situation where the state's own filing rules incorporated the relation back doctrine. We need not address this issue here, however, because we find Gonzalez's two substantive claims to be without merit. See Holland v. Florida, ___ U.S. ___, 130 S.Ct. 2549, 2560, 177 L.Ed.2d 130 (2010) ("[T]he AEDPA statute of limitations defense is not jurisdictional.") (alteration, citation, and quotation marks omitted). Thus, even if Gonzalez's federal habeas petition was timely filed, he is not entitled to relief.
Gonzalez's first substantive claim is that the Florida Supreme Court erred by concluding on direct appeal that the admission of Gonzalez's co-defendants' confessions was harmless with respect to his guilt. Specifically, the Florida Supreme Court found that the admission of the confessions of Leonardo Franqui and Pablo San Martintwo of Gonzalez's non-testifying co-defendantsviolated Gonzalez's rights under the Confrontation Clause of the Sixth Amendment.[1]See Gonzalez I, 700 So.2d at 1218-19. The Court concluded that, although this error was harmful with respect to Gonzalez's sentence, it was harmless with respect to his guilt:
[W]ith respect to guilt, we conclude that the error was harmless beyond a reasonable doubt. Not only did Gonzalez confess to participating in the robbery, he also admitted shooting the victim. He does not contest the legality of his confession in this appeal. In addition, it was determined that the fatal bullet came from the gun that Gonzalez was carrying. Gonzalez admitted being with Franqui, and an eyewitness identified Franqui as the driver of one of the stolen cars leaving the scene of the crime. Further, Franqui's fingerprints were found on one of the stolen vehicles. Moreover, Gonzalez consented to a search of his apartment which revealed $1200 of the stolen money in his bedroom closet. Thus, we conclude that there is no reasonable possibility that the erroneous admission of the confessions of Franqui and San Martin contributed to Gonzalez's conviction for felony murder.
. . . .
We agree, however, that Gonzalez's sentence must be reversed. In Franqui's confession, he said that upon approaching the bank, Gonzalez pulled out a gun and told the security guard not to move. Thereafter, he heard a shot, so he also shot his gun. He said he did not know if the shot he heard was fired by Gonzalez or the security guard, but the evidence later developed that the security guard never fired his gun. On the other hand, Gonzalez said it was Franqui who told the security guard not to move and that *1222 Franqui shot the security guard before Gonzalez shot him. He said Franqui fired three or four shots and that he only shot once. Consequently, in determining whether or not Gonzalez should be sentenced to death, we cannot say that the erroneous admission of Franqui's confession which portrayed Gonzalez as the aggressor who had precipitated the shooting was harmless beyond a reasonable doubt. Accordingly, we affirm Gonzalez's convictions but vacate the sentence of death and remand for a new penalty phase proceeding consistent with this opinion.
Id. at 1219 (emphasis in original).
Gonzalez has not shown that the Florida Supreme Court's harmless error analysis was contrary to, or an unreasonable application of, Supreme Court precedent.[2] He argues that the admission of Franqui's confession was harmful with respect to his guilt for the same reason it was harmful with respect to his sentence. But as the Florida Supreme Court explained, whether or not Gonzalez was the "aggressor who had precipitated the shooting" was legally irrelevant to his first-degree murder conviction. So long as Gonzalez participated in the robberywhich, in this case, directly resulted in the officer's deathhe would remain liable for first-degree murder under the felony murder doctrine. See Fla. Stat. § 782.04(1)(a)2.d; Lovette v. State, 636 So.2d 1304, 1307 (Fla.1994). And the evidence properly admitted at trialincluding Gonzalez's own confession, in which he admitted to shooting the victim established his participation in the robbery. Thus, we find no error in the district court's denial of this claim.
Gonzalez's second substantive claim is that the state courts erroneously disallowed two of his peremptory challenges on the ground that he failed to justify them with a non-discriminatory reason. Gonzalez I, 700 So.2d at 1218. Gonzalez's claim fails at the threshold, however, because the Supreme Court has held that the erroneous denial of a defendant's peremptory challenge presents only an issue of state law:
If a defendant is tried before a qualified jury composed of individuals not challengeable for cause, the loss of a peremptory challenge due to a state court's good-faith error is not a matter of federal constitutional concern. Rather, it is a matter for the State to address under its own laws.
... [T]his Court has consistently held that there is no freestanding constitutional right to peremptory challenges. We have characterized peremptory challenges as a creature of statute, and have made clear that a State may decline to offer them at all. When States provide peremptory challenges (as all do in some form), they confer a benefit beyond the minimum requirements of fair jury selection, and thus retain discretion to design and implement their own systems. Because peremptory challenges are within the States' province to grant or withhold, the mistaken denial of a state-provided peremptory challenge does not, without more, violate the Federal Constitution.
Rivera v. Illinois, ___ U.S. ___, 129 S.Ct. 1446, 1453-54, 173 L.Ed.2d 320 (2009) (alterations, footnote, citations, and quotation marks omitted). At oral argument, counsel for Gonzalez acknowledged Rivera, but suggested that it was inconsistent with Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. *1223 1712, 90 L.Ed.2d 69 (1986). Even if that were true, we are bound by decisions of the Supreme Court, and Gonzalez's claim falls squarely under Rivera. As a result, we find no error in the district court's denial of this claim. See Pulley v. Harris, 465 U.S. 37, 41, 104 S.Ct. 871, 79 L.Ed.2d 29 (1984) ("A federal court may not issue the writ on the basis of a perceived error of state law."). Accordingly, we affirm the district court's denial of Gonzalez's federal habeas corpus petition.
AFFIRMED.
NOTES
[1]  Only Franqui's confession is relevant here.
[2]  Our conclusion is unaffected by whether we apply Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967) (imposing a "harmless beyond a reasonable doubt" standard), or Brecht v. Abrahamson, 507 U.S. 619, 637-38, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993) (imposing an "actual prejudice" standard).
